NEET Physics Mathematical Tools, Units & Dimensions Question Bank

done Dimensions Total Questions - 142

• question_answer1)
  Select the pair whose dimensions are same
  A)
   Pressure and stress done clear
  B)
    Stress and strain done clear
  C)
  Pressure and force done clear
  D)
  Power and force done clear
  View Solution play_arrow

• question_answer2)
  Dimensional formula \[M{{L}^{-1}}{{T}^{-2}}\] does not represent the physical quantity [Manipal MEE 1995]
  A)
   Young's modulus of elasticity done clear
  B)
    Stress done clear
  C)
  Strain done clear
  D)
  Pressure done clear
  View Solution play_arrow

• question_answer3)
  Dimensional formula \[M{{L}^{2}}{{T}^{-3}}\] represents   [EAMCET 1981; MP PMT 1996, 2001]
  A)
              Force   done clear
  B)
              Power done clear
  C)
              Energy done clear
  D)
              Work done clear
  View Solution play_arrow

• question_answer4)
  The dimensions of calorie are                                                  [CPMT 1985]
  A)
              \[M{{L}^{2}}{{T}^{-2}}\]           done clear
  B)
              \[ML{{T}^{-2}}\] done clear
  C)
              \[M{{L}^{2}}{{T}^{-1}}\] done clear
  D)
                \[M{{L}^{2}}{{T}^{-3}}\] done clear
  View Solution play_arrow

• question_answer5)
  Whose dimensions is \[M{{L}^{2}}{{T}^{-1}}\]             [CPMT 1989]
  A)
              Torque done clear
  B)
              Angular momentum done clear
  C)
              Power  done clear
  D)
              Work done clear
  View Solution play_arrow

• question_answer6)
  If \[L\] and \[R\] are respectively the inductance and resistance, then the dimensions of \[\frac{L}{R}\] will be  [CPMT 1986; CBSE PMT 1988; Roorkee 1995; MP PET/PMT 1998; DCE 2002]
  A)
              \[{{M}^{0}}{{L}^{0}}{{T}^{-1}}\]      done clear
  B)
              \[{{M}^{0}}L{{T}^{0}}\] done clear
  C)
              \[{{M}^{0}}{{L}^{0}}T\] done clear
  D)
              Cannot be represented in terms of \[M,\,L\] and T done clear
  View Solution play_arrow

• question_answer7)
  Which pair has the same dimensions       [EAMCET 1982; CPMT 1984, 85; Pb. PET 2002; MP PET 1985]
  A)
   Work and power         done clear
  B)
              Density and relative density done clear
  C)
              Momentum and impulse done clear
  D)
              Stress and strain done clear
  View Solution play_arrow

• question_answer8)
  If \[C\] and \[R\] represent capacitance and resistance respectively, then the dimensions of \[RC\] are [CPMT 1981, 85; CBSE PMT 1992, 95; Pb. PMT 1999]
  A)
              \[{{M}^{0}}{{L}^{0}}{{T}^{2}}\]       done clear
  B)
              \[{{M}^{0}}{{L}^{0}}T\] done clear
  C)
              \[M{{L}^{-1}}\]       done clear
  D)
              None of the above done clear
  View Solution play_arrow

• question_answer9)
  Dimensions of one or more pairs are same. Identify the pairs                          [IIT 1986]
  A)
              Torque and work done clear
  B)
              Angular momentum and work done clear
  C)
              Energy and Young's modulus done clear
  D)
              Light year and wavelength done clear
  View Solution play_arrow

• question_answer10)
  Dimensional formula for latent heat is             [MNR 1987; CPMT 1978, 86; IIT 1983, 89; RPET 2002]
  A)
              \[{{M}^{0}}{{L}^{2}}{{T}^{-2}}\]      done clear
  B)
              \[ML{{T}^{-2}}\] done clear
  C)
              \[M{{L}^{2}}{{T}^{-2}}\] done clear
  D)
                \[M{{L}^{2}}{{T}^{-1}}\] done clear
  View Solution play_arrow

• question_answer11)
  Dimensional formula for volume elasticity is                [MP PMT 1991, 2002; CPMT 1991; MNR 1986]
  A)
              \[{{M}^{1}}{{L}^{-2}}{{T}^{-2}}\]    done clear
  B)
              \[{{M}^{1}}{{L}^{-3}}{{T}^{-2}}\] done clear
  C)
              \[{{M}^{1}}{{L}^{2}}{{T}^{-2}}\] done clear
  D)
                \[{{M}^{1}}{{L}^{-1}}{{T}^{-2}}\] done clear
  View Solution play_arrow

• question_answer12)
  The dimensions of universal gravitational constant are               [MP PMT 1984, 87, 97, 2000;  CBSE PMT 1988, 92; 2004   [MP PET 1984, 96, 99; MNR 1992; DPMT 1984; CPMT 1978, 84, 89, 90, 92, 96; AFMC 1999; NCERT 1975; DPET 1993; AIIMS 2000; RPET 2001; Pb. PMT 2002, 03; UPSEAT 1999; BCECE 2003, 05;]         
  A)
              \[{{M}^{-2}}{{L}^{2}}{{T}^{-2}}\]    done clear
  B)
              \[{{M}^{-1}}{{L}^{3}}{{T}^{-2}}\] done clear
  C)
              \[M{{L}^{-1}}{{T}^{-2}}\]          done clear
  D)
              \[M{{L}^{2}}{{T}^{-2}}\] done clear
  View Solution play_arrow

• question_answer13)
  The dimensional formula of angular velocity is                        [JIPMER 1993; AFMC 1996; AIIMS 1998]          
  A)
              \[{{M}^{0}}{{L}^{0}}{{T}^{-1}}\] done clear
  B)
              \[ML{{T}^{-1}}\] done clear
  C)
              \[{{M}^{0}}{{L}^{0}}{{T}^{1}}\] done clear
  D)
                \[M{{L}^{0}}{{T}^{-2}}\] done clear
  View Solution play_arrow

• question_answer14)
  The dimensions of power are                           [CPMT 1974, 75; SCRA 1989]
  A)
              \[{{M}^{1}}{{L}^{2}}{{T}^{-3}}\] done clear
  B)
              \[{{M}^{2}}{{L}^{1}}{{T}^{-2}}\] done clear
  C)
              \[{{M}^{1}}{{L}^{2}}{{T}^{-1}}\] done clear
  D)
                \[{{M}^{1}}{{L}^{1}}{{T}^{-2}}\] done clear
  View Solution play_arrow

• question_answer15)
  The dimensions of couple are                                      [CPMT 1972; JIPMER 1993]
  A)
              \[M{{L}^{2}}{{T}^{-2}}\] done clear
  B)
                \[ML{{T}^{-2}}\] done clear
  C)
              \[M{{L}^{-1}}{{T}^{-3}}\]          done clear
  D)
              \[M{{L}^{-2}}{{T}^{-2}}\] done clear
  View Solution play_arrow

• question_answer16)
  Dimensional formula for angular momentum is [CBSE PMT 1988, 92; EAMCET 1995; DPMT 1987; CMC Vellore 1982; CPMT 1973, 82, 86; MP PMT 1987; BHU 1995; IIT 1983; Pb. PET 2000]
  A)
              \[M{{L}^{2}}{{T}^{-2}}\]           done clear
  B)
              \[M{{L}^{2}}{{T}^{-1}}\] done clear
  C)
              \[ML{{T}^{-1}}\]     done clear
  D)
              \[{{M}^{0}}{{L}^{2}}{{T}^{-2}}\] done clear
  View Solution play_arrow

• question_answer17)
  The dimensional formula for impulse is [EAMCET 1981; CBSE PMT 1991; CPMT 1978; AFMC 1998; BCECE 2003]
  A)
              \[ML{{T}^{-2}}\]     done clear
  B)
              \[ML{{T}^{-1}}\] done clear
  C)
              \[M{{L}^{2}}{{T}^{-1}}\]           done clear
  D)
              \[{{M}^{2}}L{{T}^{-1}}\] done clear
  View Solution play_arrow

• question_answer18)
  The dimensional formula for the modulus of rigidity is                     [MNR 1984; IIT 1982; MP PET 2000]
  A)
              \[M{{L}^{2}}{{T}^{-2}}\]           done clear
  B)
              \[M{{L}^{-1}}{{T}^{-3}}\] done clear
  C)
              \[M{{L}^{-2}}{{T}^{-2}}\]          done clear
  D)
              \[M{{L}^{-1}}{{T}^{-2}}\] done clear
  View Solution play_arrow

• question_answer19)
  The dimensional formula for \[r.m.s.\] (root mean square) velocity is
  A)
   \[{{M}^{0}}L{{T}^{-1}}\] done clear
  B)
              \[{{M}^{0}}{{L}^{0}}{{T}^{-2}}\] done clear
  C)
              \[{{M}^{0}}{{L}^{0}}{{T}^{-1}}\]      done clear
  D)
              \[ML{{T}^{-3}}\] done clear
  View Solution play_arrow

• question_answer20)
  The dimensional formula for Planck's constant \[(h)\] is          [DPMT 1987; MP PMT 1983, 96; IIT 1985; MPPET 1995; AFMC 2003; RPMT 1999; Kerala PMT 2002]
  A)
              \[M{{L}^{-2}}{{T}^{-3}}\]          done clear
  B)
              \[M{{L}^{2}}{{T}^{-2}}\] done clear
  C)
              \[M{{L}^{2}}{{T}^{-1}}\] done clear
  D)
      \[M{{L}^{-2}}{{T}^{-2}}\] done clear
  View Solution play_arrow

• question_answer21)
  Out of the following, the only pair that does not have identical dimensions is   [MP PET/PMT 1998; BHU 1997]
  A)
              Angular momentum and Planck's constant done clear
  B)
              Moment of inertia and moment of a force done clear
  C)
              Work and torque done clear
  D)
              Impulse and momentum done clear
  View Solution play_arrow

• question_answer22)
  The dimensional formula for impulse is same as the dimensional formula for [CPMT 1982, 83; CBSE PMT 1993; UPSEAT 2001]
  A)
              Momentum done clear
  B)
              Force done clear
  C)
              Rate of change of momentum  done clear
  D)
              Torque done clear
  View Solution play_arrow

• question_answer23)
  Which of the following is dimensionally correct
  A)
              Pressure = Energy per unit area done clear
  B)
              Pressure = Energy per unit volume done clear
  C)
              Pressure = Force per unit volume done clear
  D)
              Pressure = Momentum per unit volume per unit time done clear
  View Solution play_arrow

• question_answer24)
  Planck's constant has the dimensions (unit) of [CPMT 1983, 84, 85, 90, 91; AIIMS 1985; MPPMT1987; EAMCET 1990; RPMT 1999; CBSE PMT 2001; MP PET 2002; KCET 2004]
  A)
              Energy done clear
  B)
              Linear momentum done clear
  C)
              Work    done clear
  D)
              Angular momentum done clear
  View Solution play_arrow

• question_answer25)
  The equation of state of some gases can be expressed as \[\left( P+\frac{a}{{{V}^{2}}} \right)\,(V-b)=RT\]. Here \[P\] is the pressure, \[V\] is the volume, \[T\] is the absolute temperature and \[a,\,b,\,R\] are constants. The dimensions of \['a'\] are [CBSE PMT 1991, 96; NCERT 1984; MP PET 1992; CPMT 1974, 79, 87, 97; MP PMT 1992, 94; MNR 1995; AFMC 1995]
  A)
              \[M{{L}^{5}}{{T}^{-2}}\]           done clear
  B)
              \[M{{L}^{-1}}{{T}^{-2}}\] done clear
  C)
              \[{{M}^{0}}{{L}^{3}}{{T}^{0}}\]       done clear
  D)
              \[{{M}^{0}}{{L}^{6}}{{T}^{0}}\] done clear
  View Solution play_arrow

• question_answer26)
  If \[V\] denotes the potential difference across the plates of a capacitor of capacitance \[C\], the dimensions of \[C{{V}^{2}}\]are                                          [CPMT 1982]
  A)
              Not expressible in \[MLT\]       done clear
  B)
              \[ML{{T}^{-2}}\] done clear
  C)
              \[{{M}^{2}}L{{T}^{-1}}\]           done clear
  D)
              \[M{{L}^{2}}{{T}^{-2}}\] done clear
  View Solution play_arrow

• question_answer27)
  If \[L\] denotes the inductance of an inductor through which a current \[i\] is flowing, the dimensions of \[L{{i}^{2}}\] are                                          [CPMT 1982, 85, 87]
  A)
              \[M{{L}^{2}}{{T}^{-2}}\]           done clear
  B)
              Not expressible in \[MLT\] done clear
  C)
              \[ML{{T}^{-2}}\]     done clear
  D)
              \[{{M}^{2}}{{L}^{2}}{{T}^{-2}}\] done clear
  View Solution play_arrow

• question_answer28)
  Of the following quantities, which one has dimensions different from the remaining three [AIIMS 1987; CBSE PMT 1993]
  A)
              Energy per unit volume            done clear
  B)
              Force per unit area done clear
  C)
              Product of voltage and charge per unit volume done clear
  D)
              Angular momentum per unit mass done clear
  View Solution play_arrow

• question_answer29)
  A spherical body of mass \[m\] and radius \[r\] is allowed to fall in a medium of viscosity \[\eta \].  The time in which the velocity of the body increases from zero to 0.63 times the terminal velocity \[(v)\] is called time constant \[(\tau )\]. Dimensionally \[\tau \] can be represented by                                                          [AIIMS 1987]
  A)
     \[\frac{m{{r}^{2}}}{6\pi \eta }\]  done clear
  B)
     \[\sqrt{\left( \frac{6\pi mr\eta }{{{g}^{2}}} \right)}\] done clear
  C)
       \[\frac{m}{6\pi \eta rv}\]    done clear
  D)
              None of the above done clear
  View Solution play_arrow

• question_answer30)
  The frequency of vibration \[f\] of a mass \[m\] suspended from a spring of spring constant \[K\]is given by a relation of this type \[f=C\,{{m}^{x}}{{K}^{y}}\]; where \[C\] is a dimensionless quantity. The value of \[x\] and \[y\] are                                                                                         [CBSE PMT 1990]
  A)
     \[x=\frac{1}{2},\,y=\frac{1}{2}\]  done clear
  B)
      \[x=-\frac{1}{2},\,y=-\frac{1}{2}\] done clear
  C)
       \[x=\frac{1}{2},\,y=-\frac{1}{2}\] done clear
  D)
         \[x=-\frac{1}{2},\,y=\frac{1}{2}\] done clear
  View Solution play_arrow

• question_answer31)
  The quantities \[A\]and \[\times \] are related by the relation, \[[ML{{T}^{-1}}]\], where \[m\] is the linear density and \[A\] is the force. The dimensions of \[B\] are of
  A)
  Pressure           done clear
  B)
  Work done clear
  C)
  Latent heat      done clear
  D)
  None of the above done clear
  View Solution play_arrow

• question_answer32)
    The velocity of water waves \[v\] may depend upon their wavelength \[\lambda \], the density of water \[\rho \] and the acceleration due to gravity \[g\]. The method of dimensions gives the relation between these quantities as [NCERT 1979; CET 1992; MP PET 2001; UPSEAT 2000]
  A)
              \[{{v}^{2}}rg\]         done clear
  B)
              \[{{v}^{2}}\propto g\lambda \rho \] done clear
  C)
              \[{{v}^{2}}\propto g\lambda \] done clear
  D)
              \[{{v}^{2}}\propto {{g}^{-1}}{{\lambda }^{-3}}\] done clear
  View Solution play_arrow

• question_answer33)
  The dimensions of Farad are                           [MP PET 1993]
  A)
              \[{{M}^{-1}}{{L}^{-2}}{{T}^{2}}{{Q}^{2}}\] done clear
  B)
              \[{{M}^{-1}}{{L}^{-2}}TQ\] done clear
  C)
              \[{{M}^{-1}}{{L}^{-2}}{{T}^{-2}}Q\]            done clear
  D)
              \[{{M}^{-1}}{{L}^{-2}}T{{Q}^{2}}\] done clear
  View Solution play_arrow

• question_answer34)
  The dimensions of resistivity in terms of \[M,\,L,\,T\] and \[Q\] where \[Q\] stands for the dimensions of charge, is [MP PET 1993]
  A)
              \[M{{L}^{3}}{{T}^{-1}}{{Q}^{-2}}\] done clear
  B)
              \[M{{L}^{3}}{{T}^{-2}}{{Q}^{-1}}\] done clear
  C)
              \[M{{L}^{2}}{{T}^{-1}}{{Q}^{-1}}\] done clear
  D)
              \[ML{{T}^{-1}}{{Q}^{-1}}\] done clear
  View Solution play_arrow

• question_answer35)
  The equation of a wave is given by \[Y=A\sin \omega \left( \frac{x}{v}-k \right)\] where \[\omega \] is the angular velocity and \[v\] is the linear velocity. The dimension of \[k\] is  [MP PMT 1993]
  A)
              \[LT\]   done clear
  B)
              \[T\] done clear
  C)
              \[{{T}^{-1}}\]          done clear
  D)
              \[{{T}^{2}}\] done clear
  View Solution play_arrow

• question_answer36)
  The dimensions of coefficient of thermal conductivity is                            [MP PMT 1993]
  A)
              \[M{{L}^{2}}{{T}^{-2}}{{K}^{-1}}\]  done clear
  B)
              \[ML{{T}^{-3}}{{K}^{-1}}\] done clear
  C)
              \[ML{{T}^{-2}}{{K}^{-1}}\]        done clear
  D)
              \[ML{{T}^{-3}}K\] done clear
  View Solution play_arrow

• question_answer37)
  Dimensional formula of stress is
  A)
              \[{{M}^{0}}L{{T}^{-2}}\]           done clear
  B)
              \[{{M}^{0}}{{L}^{-1}}{{T}^{-2}}\] done clear
  C)
              \[M{{L}^{-1}}{{T}^{-2}}\]          done clear
  D)
              \[M{{L}^{2}}{{T}^{-2}}\] done clear
  View Solution play_arrow

• question_answer38)
  Dimensional formula of velocity of sound is
  A)
              \[{{M}^{0}}L{{T}^{-2}}\]           done clear
  B)
              \[L{{T}^{0}}\] done clear
  C)
              \[{{M}^{0}}L{{T}^{-1}}\] done clear
  D)
              \[{{M}^{0}}{{L}^{-1}}{{T}^{-1}}\] done clear
  View Solution play_arrow

• question_answer39)
  Dimensional formula of capacitance is                        [CPMT 1978; MP PMT 1979; IIT 1983]
  A)
              \[{{c}^{2}}{{g}^{0}}{{p}^{-2}}\] done clear
  B)
              \[M{{L}^{2}}{{T}^{4}}{{A}^{-2}}\] done clear
  C)
              \[ML{{T}^{-4}}{{A}^{2}}\]         done clear
  D)
              \[{{M}^{-1}}{{L}^{-2}}{{T}^{-4}}{{A}^{-2}}\] done clear
  View Solution play_arrow

• question_answer40)
  \[ML{{T}^{-1}}\] represents the dimensional formula of                              [CPMT 1975]
  A)
              Power  done clear
  B)
              Momentum done clear
  C)
              Force   done clear
  D)
              Couple done clear
  View Solution play_arrow

• question_answer41)
  Dimensional formula of heat energy is                                                 [CPMT 1976, 81, 86, 91]
  A)
              \[M{{L}^{2}}{{T}^{-2}}\] done clear
  B)
              \[ML{{T}^{-1}}\] done clear
  C)
              \[{{M}^{0}}{{L}^{0}}{{T}^{-2}}\]      done clear
  D)
              None of these done clear
  View Solution play_arrow

• question_answer42)
  If \[C\] and \[L\] denote capacitance and inductance respectively, then the dimensions of \[LC\] are [CPMT 1981; MP PET 1997]          
  A)
              \[{{M}^{0}}{{L}^{0}}{{T}^{0}}\]       done clear
  B)
              \[{{M}^{0}}{{L}^{0}}{{T}^{2}}\] done clear
  C)
              \[{{M}^{2}}{{L}^{0}}{{T}^{2}}\]       done clear
  D)
              \[ML{{T}^{2}}\] done clear
  View Solution play_arrow

• question_answer43)
  Which of the following quantities has the same dimensions as that of energy [AFMC 1991; CPMT 1976; DPMT 2001]
  A)
              Power  done clear
  B)
              Force done clear
  C)
              Momentum      done clear
  D)
              Work done clear
  View Solution play_arrow

• question_answer44)
  The dimensions of "time constant" \[\frac{L}{R}\] during growth and decay of current in all inductive circuit is same as that of                                                                         [MP PET 1993; EAMCET 1994]
  A)
              Constant          done clear
  B)
              Resistance done clear
  C)
              Current            done clear
  D)
              Time done clear
  View Solution play_arrow

• question_answer45)
  The period of a body under SHM i.e. presented by \[T={{P}^{a}}{{D}^{b}}{{S}^{c}}\]; where \[P\] is pressure, \[D\] is density and \[S\] is surface tension. The value of \[a,\,b\] and \[c\] are  [CPMT 1981]
  A)
              \[-\frac{3}{2},\,\frac{1}{2},\,1\]        done clear
  B)
              \[-1,\,-2,\,3\] done clear
  C)
              \[\frac{1}{2},\,-\frac{3}{2},\,-\frac{1}{2}\]  done clear
  D)
              \[1,\,2,\,\frac{1}{3}\] done clear
  View Solution play_arrow

• question_answer46)
  Which of the following pairs of physical quantities has the same dimensions   [CPMT 1978; NCERT 1987]
  A)
              Work and power          done clear
  B)
              Momentum and energy done clear
  C)
              Force and power done clear
  D)
                Work and energy done clear
  View Solution play_arrow

• question_answer47)
  The velocity of a freely falling body changes as \[{{g}^{p}}{{h}^{q}}\] where g is acceleration due to gravity and \[h\] is the height. The values of \[p\] and \[q\] are            [NCERT 1983; EAMCET 1994]
  A)
     \[1,\frac{1}{2}\]       done clear
  B)
      \[{{M}^{0}}{{L}^{2}}{{T}^{-2}}\] done clear
  C)
       \[\frac{1}{2},\,1\]   done clear
  D)
              \[1,\,1\] done clear
  View Solution play_arrow

• question_answer48)
  Which one of the following does not have the same dimensions                                     [CPMT 1985]
  A)
              Work and energy done clear
  B)
              Angle and strain done clear
  C)
              Relative density and refractive index done clear
  D)
              Planck constant and energy done clear
  View Solution play_arrow

• question_answer49)
  Dimensions of frequency are                                                               [CPMT 1988]
  A)
              \[{{M}^{0}}{{L}^{-1}}{{T}^{0}}\]      done clear
  B)
              \[{{M}^{0}}{{L}^{0}}{{T}^{-1}}\] done clear
  C)
              \[{{M}^{0}}{{L}^{0}}T\] done clear
  D)
                \[M{{T}^{-2}}\] done clear
  View Solution play_arrow

• question_answer50)
  Which one has the dimensions different from the remaining three                               [CBSE PMT 1988]
  A)
              Power done clear
  B)
              Work done clear
  C)
              Torque done clear
  D)
              Energy done clear
  View Solution play_arrow

• question_answer51)
  A small steel ball of radius \[r\] is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity \[\eta \]. After some time the velocity of the ball attains a constant value known as terminal velocity \[{{v}_{T}}\]. The terminal velocity depends on (i) the mass of the ball \[m\], (ii) \[\eta \], (iii) \[r\] and (iv) acceleration due to gravity \[g\]. Which of the following relations is dimensionally correct [CPMT 1992; CBSE PMT 1992; NCERT 1983; MP PMT 2001]
  A)
     \[{{v}_{T}}\propto \frac{mg}{\eta r}\]       done clear
  B)
     \[{{v}_{T}}\propto \frac{\eta r}{mg}\] done clear
  C)
              \[{{v}_{T}}\propto \eta rmg\] done clear
  D)
                \[{{v}_{T}}\propto \frac{mgr}{\eta }\] done clear
  View Solution play_arrow

• question_answer52)
  The quantity \[X=\frac{{{\varepsilon }_{0}}LV}{t}\]: \[{{\varepsilon }_{0}}\] is the permittivity of free space, \[L\]is length, \[V\] is potential difference and \[t\] is time. The dimensions of \[X\]  are same as that of [IIT 2001]
  A)
              Resistance       done clear
  B)
              Charge done clear
  C)
              Voltage done clear
  D)
              Current done clear
  View Solution play_arrow

• question_answer53)
  \[{{\mu }_{0}}\] and \[{{\varepsilon }_{0}}\] denote the permeability and permittivity of free space, the dimensions of \[{{\mu }_{0}}{{\varepsilon }_{0}}\] are
  A)
              \[L{{T}^{-1}}\]        done clear
  B)
              \[{{L}^{-2}}{{T}^{2}}\] done clear
  C)
              \[{{M}^{-1}}{{L}^{-3}}{{Q}^{2}}{{T}^{2}}\]        done clear
  D)
              \[{{M}^{-1}}{{L}^{-3}}{{I}^{2}}{{T}^{2}}\] done clear
  View Solution play_arrow

• question_answer54)
  The expression \[[M{{L}^{2}}{{T}^{-2}}]\] represents                            [JIPMER 1993, 97]
  A)
              Pressure           done clear
  B)
              Kinetic energy done clear
  C)
              Momentum      done clear
  D)
              Power done clear
  View Solution play_arrow

• question_answer55)
  The dimensions of physical quantity \[X\] in the equation Force \[=\frac{X}{\text{Density}}\] is given by   [DCE 1993]
  A)
              \[{{M}^{1}}{{L}^{4}}{{T}^{-2}}\]      done clear
  B)
              \[{{M}^{2}}{{L}^{-2}}{{T}^{-1}}\] done clear
  C)
              \[{{M}^{2}}{{L}^{-2}}{{T}^{-2}}\]    done clear
  D)
              \[{{M}^{1}}{{L}^{-2}}{{T}^{-1}}\] done clear
  View Solution play_arrow

• question_answer56)
  The dimensions of \[C{{V}^{2}}\] matches with the dimensions of                                     [DCE 1993]
  A)
              \[{{L}^{2}}I\]           done clear
  B)
              \[{{L}^{2}}{{I}^{2}}\] done clear
  C)
              \[L{{I}^{2}}\]           done clear
  D)
              \[\frac{1}{LI}\] done clear
  View Solution play_arrow

• question_answer57)
  The Martians use force \[(F)\], acceleration \[(A)\] and time \[(T)\] as their fundamental physical quantities. The dimensions of length on Martians system are                                                               [DCE 1993]
  A)
              \[F{{T}^{2}}\]         done clear
  B)
              \[{{F}^{-1}}{{T}^{2}}\] done clear
  C)
              \[{{F}^{-1}}{{A}^{2}}{{T}^{-1}}\] done clear
  D)
                \[A{{T}^{2}}\] done clear
  View Solution play_arrow

• question_answer58)
  The dimension of \[\frac{1}{\sqrt{{{\varepsilon }_{0}}{{\mu }_{0}}}}\] is that of            [SCRA 1986]
  A)
              Velocity done clear
  B)
                Time done clear
  C)
              Capacitance done clear
  D)
                Distance done clear
  View Solution play_arrow

• question_answer59)
  An athletic coach told his team that muscle times speed equals power. What dimensions does he view for muscle
  A)
              \[ML{{T}^{-2}}\] done clear
  B)
              \[M{{L}^{2}}{{T}^{-2}}\] done clear
  C)
              \[ML{{T}^{2}}\]      done clear
  D)
              \[L\] done clear
  View Solution play_arrow

• question_answer60)
  The foundations of dimensional analysis were laid down by
  A)
              Gallileo            done clear
  B)
              Newton done clear
  C)
              Fourier done clear
  D)
              Joule done clear
  View Solution play_arrow

• question_answer61)
  The dimensional formula of wave number is
  A)
              \[{{M}^{0}}{{L}^{0}}{{T}^{-1}}\]      done clear
  B)
              \[{{M}^{0}}{{L}^{-1}}{{T}^{0}}\] done clear
  C)
              \[{{M}^{-1}}{{L}^{-1}}{{T}^{0}}\]    done clear
  D)
              \[{{M}^{0}}{{L}^{0}}{{T}^{0}}\] done clear
  View Solution play_arrow

• question_answer62)
  The dimensions of stress are equal to  [MP PET 1991, 2003]
  A)
              Force   done clear
  B)
              Pressure done clear
  C)
              Work    done clear
  D)
         \[\frac{1}{\text{Pressure}}\] done clear
  View Solution play_arrow

• question_answer63)
  The dimensions of pressure are                                      [CPMT 1977; MP PMT 1994]
  A)
              \[ML{{T}^{-2}}\]     done clear
  B)
              \[M{{L}^{-2}}{{T}^{2}}\] done clear
  C)
              \[M{{L}^{-1}}{{T}^{-2}}\] done clear
  D)
              \[ML{{T}^{2}}\] done clear
  View Solution play_arrow

• question_answer64)
  Dimensions of permeability are                                   [CBSE PMT 1991; AIIMS 2003]
  A)
              \[{{A}^{-2}}{{M}^{1}}{{L}^{1}}{{T}^{-2}}\] done clear
  B)
              \[ML{{T}^{-2}}\] done clear
  C)
              \[M{{L}^{0}}{{T}^{-1}}\] done clear
  D)
                \[{{A}^{-1}}ML{{T}^{2}}\] done clear
  View Solution play_arrow

• question_answer65)
  Dimensional formula of magnetic flux is [DCE 1993; IIT 1982; CBSE PMT 1989, 99; DPMT 2001; Kerala PMT 2005]
  A)
              \[M{{L}^{2}}{{T}^{-2}}{{A}^{-1}}\]  done clear
  B)
              \[M{{L}^{0}}{{T}^{-2}}{{A}^{-2}}\] done clear
  C)
              \[{{M}^{0}}{{L}^{-2}}{{T}^{-2}}{{A}^{-3}}\] done clear
  D)
                \[M{{L}^{2}}{{T}^{-2}}{{A}^{3}}\] done clear
  View Solution play_arrow

• question_answer66)
  If \[P\] represents radiation pressure, \[c\] represents speed of light and \[Q\] represents radiation energy striking a unit area per second, then non-zero integers \[x,\,y\] and \[z\] such that \[{{P}^{x}}{{Q}^{y}}{{c}^{z}}\] is dimensionless, are                                 [AFMC 1991; CBSE PMT 1992; CPMT 1981, 92; MP PMT 1992]
  A)
              \[x=1,\,\,y=1,\,\,z=-1\] done clear
  B)
                \[x=1,\,y=-1,\,z=1\] done clear
  C)
              \[x=-1,\,y=1,\,z=1\]    done clear
  D)
              \[x=1,\,y=1,\,z=1\] done clear
  View Solution play_arrow

• question_answer67)
  Inductance \[L\] can be dimensionally represented as               [CBSE PMT 1989, 92; IIT 1983; CPMT 1992; DPMT 1999; KCET 2004; J&K CET 2005]
  A)
              \[M{{L}^{2}}{{T}^{-2}}{{A}^{-2}}\]  done clear
  B)
              \[M{{L}^{2}}{{T}^{-4}}{{A}^{-3}}\] done clear
  C)
              \[M{{L}^{-2}}{{T}^{-2}}{{A}^{-2}}\] done clear
  D)
              \[M{{L}^{2}}{{T}^{4}}{{A}^{3}}\] done clear
  View Solution play_arrow

• question_answer68)
  Dimensions of strain are          [MP PET 1984; SCRA 1986]
  A)
    \[ML{{T}^{-1}}\]   done clear
  B)
      \[M{{L}^{2}}{{T}^{-1}}\] done clear
  C)
              \[ML{{T}^{-2}}\]     done clear
  D)
              \[{{M}^{0}}{{L}^{0}}{{T}^{0}}\] done clear
  View Solution play_arrow

• question_answer69)
  Dimensions of time in power are                     [EAMCET 1982]
  A)
              \[{{T}^{-1}}\]          done clear
  B)
              \[{{T}^{-2}}\] done clear
  C)
              \[{{T}^{-3}}\] done clear
  D)
              \[{{T}^{0}}\] done clear
  View Solution play_arrow

• question_answer70)
  Dimensions of kinetic energy are                                               [Bihar PET 1983; DPET 1993; AFMC 1991]
  A)
              \[M{{L}^{2}}{{T}^{-2}}\] done clear
  B)
              \[{{M}^{2}}L{{T}^{-1}}\] done clear
  C)
              \[M{{L}^{2}}{{T}^{-1}}\]           done clear
  D)
              \[M{{L}^{3}}{{T}^{-1}}\] done clear
  View Solution play_arrow

• question_answer71)
  Dimensional formula for torque is [DPMT 1984; IIT 1983; CBSE PMT 1990; MNR 1988; AIIMS 2002; BHU 1995, 2001; RPMT 1999; RPET 2003; DCE 1999, 2000; DCE 2004]
  A)
              \[{{L}^{2}}M{{T}^{-2}}\]           done clear
  B)
              \[{{L}^{-1}}M{{T}^{-2}}\] done clear
  C)
              \[{{L}^{2}}M{{T}^{-3}}\]           done clear
  D)
              \[LM{{T}^{-2}}\] done clear
  View Solution play_arrow

• question_answer72)
  Dimensions of coefficient of viscosity are [AIIMS 1993; CPMT 1992; Bihar PET 1984; MP PMT 1987, 89, 91; AFMC 1986;  CBSE PMT 1992; KCET 1994; DCE 1999; AIEEE 2004; DPMT 2004]
  A)
              \[M{{L}^{2}}{{T}^{-2}}\]           done clear
  B)
              \[M{{L}^{2}}{{T}^{-1}}\] done clear
  C)
              \[M{{L}^{-1}}{{T}^{-1}}\]          done clear
  D)
              \[MLT\] done clear
  View Solution play_arrow

• question_answer73)
  The dimension of quantity \[(L/RCV)\] is         [Roorkee 1994]
  A)
              \[[A]\]   done clear
  B)
              \[[{{A}^{2}}]\] done clear
  C)
              \[[{{A}^{-1}}]\]        done clear
  D)
              None of these done clear
  View Solution play_arrow

• question_answer74)
  The dimension of the ratio of angular to linear momentum is                          [MNR 1994]
  A)
              \[{{M}^{0}}{{L}^{1}}{{T}^{0}}\]       done clear
  B)
              \[{{M}^{1}}{{L}^{1}}{{T}^{-1}}\] done clear
  C)
              \[{{M}^{1}}{{L}^{2}}{{T}^{-1}}\]      done clear
  D)
              \[{{M}^{-1}}{{L}^{-1}}{{T}^{-1}}\] done clear
  View Solution play_arrow

• question_answer75)
  The pair having the same dimensions is                      [MP PET 1994; CPMT 1996]
  A)
              Angular momentum, work       done clear
  B)
              Work, torque done clear
  C)
              Potential energy, linear momentum done clear
  D)
              Kinetic energy, velocity done clear
  View Solution play_arrow

• question_answer76)
  The dimensions of surface tension are                                     [MP PMT 1994, 99; UPSEAT 1999]
  A)
              \[M{{L}^{-1}}{{T}^{-2}}\]          done clear
  B)
              \[ML{{T}^{-2}}\] done clear
  C)
              \[M{{L}^{-1}}{{T}^{-1}}\]          done clear
  D)
              \[M{{T}^{-2}}\] done clear
  View Solution play_arrow

• question_answer77)
  In the following list, the only pair which have different dimensions, is                          [Manipal MEE 1995]
  A)
              Linear momentum and moment of a force done clear
  B)
              Planck's constant and angular momentum done clear
  C)
              Pressure and modulus of elasticity done clear
  D)
              Torque and potential energy done clear
  View Solution play_arrow

• question_answer78)
  If \[R\] and \[L\] represent respectively resistance and self-inductance, which of the following combinations has the dimensions of frequency                                                  [MP PMT 1996, 2000, 02; MP PET 1999]
  A)
              \[\frac{R}{L}\]            done clear
  B)
              \[\frac{L}{R}\] done clear
  C)
              \[\sqrt{\frac{R}{L}}\] done clear
  D)
              \[\sqrt{\frac{L}{R}}\] done clear
  View Solution play_arrow

• question_answer79)
  If velocity \[v\], acceleration \[A\] and force \[F\] are chosen as fundamental quantities, then the dimensional formula of angular momentum  in terms of \[v,\,A\] and \[F\] would be
  A)
              \[F{{A}^{-1}}v\]      done clear
  B)
              \[F{{v}^{3}}{{A}^{-2}}\] done clear
  C)
  \[F{{v}^{2}}{{A}^{-1}}\] done clear
  D)
  \[{{F}^{2}}{{v}^{2}}{{A}^{-1}}\] done clear
  View Solution play_arrow

• question_answer80)
  The dimensions of permittivity \[{{\varepsilon }_{0}}\] are   [MP PET 1997; AIIMS-2004; DCE-2003]
  A)
              \[{{A}^{2}}{{T}^{2}}{{M}^{-1}}{{L}^{-3}}\]        done clear
  B)
              \[{{A}^{2}}{{T}^{4}}{{M}^{-1}}{{L}^{-3}}\] done clear
  C)
              \[{{A}^{-2}}{{T}^{-4}}M{{L}^{3}}\]  done clear
  D)
              \[{{A}^{2}}{{T}^{-4}}{{M}^{-1}}{{L}^{-3}}\] done clear
  View Solution play_arrow

• question_answer81)
  Dimensions of the following three quantities are the same             [MP PET 1997]
  A)
              Work, energy, force done clear
  B)
              Velocity, momentum, impulse done clear
  C)
              Potential energy, kinetic energy, momentum done clear
  D)
              Pressure, stress, coefficient of elasticity done clear
  View Solution play_arrow

• question_answer82)
  The dimensions of Planck's constant and angular momentum are respectively       [CPMT 1999; BCECE 2004]
  A)
              \[M{{L}^{2}}{{T}^{-1}}\] and \[ML{{T}^{-1}}\]        done clear
  B)
              \[M{{L}^{2}}{{T}^{-1}}\] and \[M{{L}^{2}}{{T}^{-1}}\] done clear
  C)
              \[ML{{T}^{-1}}\] and \[M{{L}^{2}}{{T}^{-1}}\]        done clear
  D)
              \[ML{{T}^{-1}}\] and \[M{{L}^{2}}{{T}^{-2}}\] done clear
  View Solution play_arrow

• question_answer83)
  Let \[[{{\varepsilon }_{0}}]\] denotes the dimensional formula of the permittivity of the vacuum and \[[{{\mu }_{0}}]\] that of the permeability of the vacuum. If \[M=\text{mass}\], \[L=\text{length}\], \[T=\text{Time}\] and \[I=\text{electric current}\], then                                 [IIT 1998]
  A)
              \[[{{\varepsilon }_{0}}]={{M}^{-1}}{{L}^{-3}}{{T}^{2}}I\]            done clear
  B)
              \[[{{\varepsilon }_{0}}]={{M}^{-1}}{{L}^{-3}}{{T}^{4}}{{I}^{2}}\] done clear
  C)
              \[[{{\mu }_{0}}]=ML{{T}^{-2}}{{I}^{-2}}\]    done clear
  D)
              \[[{{\mu }_{0}}]=M{{L}^{2}}{{T}^{-1}}I\] done clear
  View Solution play_arrow

• question_answer84)
  Dimensions of \[CR\] are those of                                [EAMCET (Engg.) 1995; AIIMS 1999]
  A)
              Frequency        done clear
  B)
              Energy done clear
  C)
              Time period     done clear
  D)
              Current done clear
  View Solution play_arrow

• question_answer85)
  The physical quantity that has no dimensions                                     [EAMCET (Engg.) 1995]
  A)
              Angular Velocity          done clear
  B)
              Linear momentum done clear
  C)
              Angular momentum     done clear
  D)
              Strain done clear
  View Solution play_arrow

• question_answer86)
  \[M{{L}^{-1}}{{T}^{-2}}\] represents              [EAMCET (Med.) 1995; Pb. PMT 2001]
  A)
              Stress   done clear
  B)
              Young's Modulus done clear
  C)
              Pressure done clear
  D)
                All the above three quantities done clear
  View Solution play_arrow

• question_answer87)
  Dimensions of magnetic field intensity is                     [RPMT 1997; EAMCET (Med.) 2000; MP PET 2003]
  A)
              \[[{{M}^{0}}{{L}^{-1}}{{T}^{0}}{{A}^{1}}]\]       done clear
  B)
              \[[ML{{T}^{-1}}{{A}^{-1}}]\] done clear
  C)
              \[[M{{L}^{0}}{{T}^{-2}}{{A}^{-1}}]\] done clear
  D)
              \[[ML{{T}^{-2}}A]\] done clear
  View Solution play_arrow

• question_answer88)
  The force \[F\] on a sphere of radius \['a'\] moving in a medium with velocity \['v'\] is given by \[F=6\pi \eta av\]. The dimensions of \[\eta \] are                  [CBSE PMT 1997; DPMT 2000]
  A)
              \[M{{L}^{-1}}{{T}^{-1}}\] done clear
  B)
              \[M{{T}^{-1}}\] done clear
  C)
              \[ML{{T}^{-2}}\] done clear
  D)
                \[M{{L}^{-3}}\] done clear
  View Solution play_arrow

• question_answer89)
  Which physical quantities have the same dimension                                [CPMT 1997]
  A)
              Couple of force and work       done clear
  B)
              Force and power done clear
  C)
              Latent heat and specific heat   done clear
  D)
              Work and power done clear
  View Solution play_arrow

• question_answer90)
  Two quantities A and B have different dimensions. Which mathematical operation given below is physically meaningful                               [CPMT 1997]
  A)
              \[A/B\] done clear
  B)
              \[A+B\] done clear
  C)
              \[A-B\] done clear
  D)
              None done clear
  View Solution play_arrow

• question_answer91)
  Given that \[v\] is speed, \[r\] is the radius and \[g\] is the acceleration due to gravity. Which of the following is dimensionless                          [CET 1998]
  A)
              \[{{v}^{2}}/rg\]        done clear
  B)
              \[{{v}^{2}}r/g\] done clear
  C)
              \[{{v}^{2}}g/r\]        done clear
  D)
              \[{{v}^{2}}rg\] done clear
  View Solution play_arrow

• question_answer92)
  The physical quantity which has the dimensional formula \[{{M}^{1}}{{T}^{-3}}\] is     [CET 1998]
  A)
              Surface tension            done clear
  B)
              Solar constant done clear
  C)
              Density done clear
  D)
              Compressibility done clear
  View Solution play_arrow

• question_answer93)
  A force \[F\] is given by \[F=at+b{{t}^{2}}\], where \[t\] is time. What are the dimensions of \[a\] and \[b\]  [AFMC 2001; BHU 1998, 2005]
  A)
              \[ML{{T}^{-3}}\] and \[M{{L}^{2}}{{T}^{-4}}\]        done clear
  B)
              \[ML{{T}^{-3}}\] and \[ML{{T}^{-4}}\] done clear
  C)
              \[ML{{T}^{-1}}\] and \[ML{{T}^{0}}\]   done clear
  D)
              \[ML{{T}^{-4}}\] and \[ML{{T}^{1}}\] done clear
  View Solution play_arrow

• question_answer94)
  The dimensions of inter atomic force constant are                                           [UPSEAT 1999]
  A)
              \[M{{T}^{-2}}\] done clear
  B)
              \[ML{{T}^{-1}}\] done clear
  C)
              \[ML{{T}^{-2}}\] done clear
  D)
                \[M{{L}^{-1}}{{T}^{-1}}\] done clear
  View Solution play_arrow

• question_answer95)
  If the speed of light \[(c)\], acceleration due to gravity \[(g)\] and pressure \[(p)\] are taken as the fundamental quantities, then the dimension of gravitational constant is                                           [AMU (Med.) 1999]
  A)
              \[{{c}^{2}}{{g}^{0}}{{p}^{-2}}\]        done clear
  B)
              \[{{c}^{0}}{{g}^{2}}{{p}^{-1}}\] done clear
  C)
              \[c{{g}^{3}}{{p}^{-2}}\] done clear
  D)
              \[{{c}^{-1}}{{g}^{0}}{{p}^{-1}}\] done clear
  View Solution play_arrow

• question_answer96)
  If the time period \[(T)\]  of vibration of a liquid drop depends on surface tension \[(S)\], radius \[(r)\]  of the drop and density \[(\rho )\] of the liquid, then the expression of \[T\] is                    [AMU (Med.) 2000]
  A)
              \[T=k\sqrt{\rho {{r}^{3}}/S}\] done clear
  B)
              \[T=k\sqrt{{{\rho }^{1/2}}{{r}^{3}}/S}\] done clear
  C)
              \[T=k\sqrt{\rho {{r}^{3}}/{{S}^{1/2}}}\]           done clear
  D)
              None of these done clear
  View Solution play_arrow

• question_answer97)
  \[M{{L}^{3}}{{T}^{-1}}{{Q}^{-2}}\] is dimension of                                                 [RPET 2000]
  A)
              Resistivity        done clear
  B)
              Conductivity done clear
  C)
              Resistance       done clear
  D)
              None of these done clear
  View Solution play_arrow

• question_answer98)
  Dimension of electric current is                        [CBSE PMT 2000]
  A)
              \[[{{M}^{0}}{{L}^{0}}{{T}^{-1}}Q]\]            done clear
  B)
              \[[M{{L}^{2}}{{T}^{-1}}Q]\] done clear
  C)
              \[[{{M}^{2}}L{{T}^{-1}}Q]\]      done clear
  D)
              \[[{{M}^{2}}{{L}^{2}}{{T}^{-1}}Q]\] done clear
  View Solution play_arrow

• question_answer99)
  The fundamental physical quantities that have same dimensions in the dimensional formulae of torque and angular momentum are                                                                        [EAMCET (Eng.) 2000]
  A)
              Mass, time       done clear
  B)
              Time, length done clear
  C)
              Mass, length done clear
  D)
              Time, mole done clear
  View Solution play_arrow

• question_answer100)
  If pressure \[P\], velocity \[V\] and time \[T\] are taken as fundamental physical quantities, the dimensional formula of force is                                                                                             [EAMCET (Eng.) 2000]
  A)
              \[P{{V}^{2}}{{T}^{2}}\] done clear
  B)
              \[{{P}^{-1}}{{V}^{2}}{{T}^{-2}}\] done clear
  C)
              \[PV{{T}^{2}}\]       done clear
  D)
              \[{{P}^{-1}}V{{T}^{2}}\] done clear
  View Solution play_arrow

• question_answer101)
  The physical quantity which has dimensional formula as that of \[\frac{\text{Energy}}{\text{Mass}\times \text{Length}}\] is                                                                                           [EAMCET (Eng.) 2000]
  A)
              Force   done clear
  B)
              Power done clear
  C)
              Pressure           done clear
  D)
              Acceleration done clear
  View Solution play_arrow

• question_answer102)
  If energy \[(E)\], velocity \[(v)\]and force \[(F)\] be taken as fundamental quantity, then what are the dimensions of mass                                                                                                                [AMU 2000]
  A)
              \[E{{v}^{2}}\]          done clear
  B)
              \[E{{v}^{-2}}\] done clear
  C)
              \[F{{v}^{-1}}\]         done clear
  D)
              \[F{{v}^{-2}}\] done clear
  View Solution play_arrow

• question_answer103)
  Dimensions of luminous flux are                      [UPSEAT 2001]
  A)
              \[M{{L}^{2}}{{T}^{-2}}\]           done clear
  B)
              \[M{{L}^{2}}{{T}^{-3}}\] done clear
  C)
              \[M{{L}^{2}}{{T}^{-1}}\] done clear
  D)
                \[ML{{T}^{-2}}\] done clear
  View Solution play_arrow

• question_answer104)
  A physcial quantity \[x\] depends on quantities \[y\] and \[z\] as follows: \[x=Ay+B\tan Cz\], where \[A,\,B\] and \[C\]  are constants. Which of the following do not have the same dimensions            [AMU (Engg.) 2001]
  A)
              \[x\] and \[B\]   done clear
  B)
              \[C\] and \[{{z}^{-1}}\] done clear
  C)
              \[y\] and \[B/A\]           done clear
  D)
              \[x\] and \[A\] done clear
  View Solution play_arrow

• question_answer105)
  Which of the following pair does not have similar dimensions                                     [AIIMS 2001]
  A)
              Stress and pressure done clear
  B)
                Angle and strain done clear
  C)
              Tension and surface tension done clear
  D)
              Planck's constant and angular momentum done clear
  View Solution play_arrow

• question_answer106)
  Out of the following which pair of quantities do not have same dimensions                            [RPET 2001]
  A)
              Planck's constant and angular momentum done clear
  B)
              Work and energy done clear
  C)
              Pressure and Young's modulus done clear
  D)
              Torque & moment of inertia done clear
  View Solution play_arrow

• question_answer107)
  Identify the pair which has different dimensions                                              [KCET 2001]
  A)
              Planck's constant and angular momentum done clear
  B)
              Impulse and linear momentum done clear
  C)
              Angular momentum and frequency done clear
  D)
              Pressure and Young's modulus done clear
  View Solution play_arrow

• question_answer108)
  The dimensional formula \[{{M}^{0}}{{L}^{2}}{{T}^{-2}}\] stands for                     [KCET 2001]
  A)
              Torque done clear
  B)
              Angular momentum done clear
  C)
              Latent heat done clear
  D)
              Coefficient of thermal conductivity done clear
  View Solution play_arrow

• question_answer109)
  Which of the following represents the dimensions of Farad                  [AMU (Med.) 2002]
  A)
              \[{{M}^{-1}}{{L}^{-2}}{{T}^{4}}{{A}^{2}}\] done clear
  B)
              \[M{{L}^{2}}{{T}^{2}}{{A}^{-2}}\] done clear
  C)
              \[M{{L}^{2}}{{T}^{2}}{{A}^{-1}}\]   done clear
  D)
              \[M{{T}^{-2}}{{A}^{-1}}\] done clear
  View Solution play_arrow

• question_answer110)
  If \[L,\,C\] and \[R\] denote the inductance, capacitance and resistance respectively, the dimensional formula for \[{{C}^{2}}LR\] is                                                                           [UPSEAT 2002]
  A)
              \[[M{{L}^{-2}}{{T}^{-1}}{{I}^{0}}]\] done clear
  B)
              \[[{{M}^{0}}{{L}^{0}}{{T}^{3}}{{I}^{0}}]\] done clear
  C)
              \[[{{M}^{-1}}{{L}^{-2}}{{T}^{6}}{{I}^{2}}]\]       done clear
  D)
              \[[{{M}^{0}}{{L}^{0}}{{T}^{2}}{{I}^{0}}]\] done clear
  View Solution play_arrow

• question_answer111)
  If the velocity of light \[(c)\], gravitational constant \[(G)\] and Planck's constant \[(h)\] are chosen as fundamental units, then the dimensions of mass in new system is                                        [UPSEAT 2002]
  A)
              \[{{c}^{1/2}}{{G}^{1/2}}{{h}^{1/2}}\]           done clear
  B)
              \[{{c}^{1/2}}{{G}^{1/2}}{{h}^{-1/2}}\] done clear
  C)
              \[{{c}^{1/2}}{{G}^{-1/2}}{{h}^{1/2}}\] done clear
  D)
              \[{{c}^{-1/2}}{{G}^{1/2}}{{h}^{1/2}}\] done clear
  View Solution play_arrow

• question_answer112)
  Dimensions of charge are?                                                                  [DPMT 2002]
  A)
              \[{{M}^{0}}{{L}^{0}}{{T}^{-1}}{{A}^{-1}}\]        done clear
  B)
              \[MLT{{A}^{-1}}\] done clear
  C)
              \[{{T}^{-1}}A\]        done clear
  D)
              \[TA\] done clear
  View Solution play_arrow

• question_answer113)
  According to Newton, the viscous force acting between liquid layers of area A and velocity gradient \[\Delta v/\Delta z\] is given by \[F=-\eta A\frac{\Delta v}{\Delta z}\] where \[\eta \] is constant called coefficient of viscosity. The dimension of \[\eta \] are?                                                                                [JIPMER 2001, 02]
  A)
              \[[M{{L}^{2}}{{T}^{-2}}]\]         done clear
  B)
              \[[M{{L}^{-1}}{{T}^{-1}}]\] done clear
  C)
              \[[M{{L}^{-2}}{{T}^{-2}}]\]        done clear
  D)
              \[[{{M}^{0}}{{L}^{0}}{{T}^{0}}]\] done clear
  View Solution play_arrow

• question_answer114)
  Identify the pair whose dimensions are equal?                                                             [AIEEE 2002]
  A)
   Torque and work        done clear
  B)
              Stress and energy done clear
  C)
              Force and stress           done clear
  D)
              Force and work done clear
  View Solution play_arrow

• question_answer115)
  The dimensions of pressure is equal to?                                                                       [AIEEE 2002]
  A)
              Force per unit volume done clear
  B)
              Energy per unit volume done clear
  C)
              Force done clear
  D)
              Energy done clear
  View Solution play_arrow

• question_answer116)
  Which of the two have same dimensions?                                                       [AIEEE 2002]
  A)
              Force and strain          done clear
  B)
              Force and stress done clear
  C)
              Angular velocity and frequency done clear
  D)
              Energy and strain done clear
  View Solution play_arrow

• question_answer117)
  An object is moving through the liquid. The viscous damping force acting on it is proportional to the velocity. Then dimension of constant of proportionality is?                                        [Orissa JEE 2002]
  A)
              \[M{{L}^{-1}}{{T}^{-1}}\] done clear
  B)
                \[ML{{T}^{-1}}\] done clear
  C)
              \[{{M}^{0}}L{{T}^{-1}}\] done clear
  D)
                \[M{{L}^{0}}{{T}^{-1}}\] done clear
  View Solution play_arrow

• question_answer118)
  The dimensions of emf in MKS is?                                                       [CPMT 2002]
  A)
              \[M{{L}^{-1}}{{T}^{-2}}{{Q}^{-2}}\] done clear
  B)
                \[M{{L}^{2}}{{T}^{-2}}{{Q}^{-2}}\] done clear
  C)
              \[ML{{T}^{-2}}{{Q}^{-1}}\] done clear
  D)
                \[M{{L}^{2}}{{T}^{-2}}{{Q}^{-1}}\] done clear
  View Solution play_arrow

• question_answer119)
  Which of the following quantities is dimensionless?                                  [MP PET 2002]
  A)
              Gravitational constant done clear
  B)
              Planck's constant done clear
  C)
              Power of a convex lens            done clear
  D)
              None done clear
  View Solution play_arrow

• question_answer120)
  The dimensional formula for Boltzmann's constant is?                               [MP PET 2002; Pb. PET 2001]
  A)
              \[[M{{L}^{2}}{{T}^{-2}}{{\theta }^{-1}}]\] done clear
  B)
                \[[M{{L}^{2}}{{T}^{-2}}]\] done clear
  C)
              \[[M{{L}^{0}}{{T}^{-2}}{{\theta }^{-1}}]\] done clear
  D)
                \[[M{{L}^{-2}}{{T}^{-1}}{{\theta }^{-1}}]\] done clear
  View Solution play_arrow

• question_answer121)
  The dimensions of \[K\] in the equation \[W=\frac{1}{2}\,\,K{{x}^{2}}\] is?       [Orissa JEE 2003]
  A)
              \[{{M}^{1}}{{L}^{0}}{{T}^{-2}}\] done clear
  B)
                \[{{M}^{0}}{{L}^{1}}{{T}^{-1}}\] done clear
  C)
              \[{{M}^{1}}{{L}^{1}}{{T}^{-2}}\] done clear
  D)
                \[{{M}^{1}}{{L}^{0}}{{T}^{-1}}\] done clear
  View Solution play_arrow

• question_answer122)
  The physical quantities not having same dimensions are?                                  [AIEEE 2003]
  A)
              Speed and \[{{({{\mu }_{0}}{{\varepsilon }_{0}})}^{-1/2}}\] done clear
  B)
                          Torque and work             done clear
  C)
                          Momentum and Planck's constant             done clear
  D)
                          Stress and Young's modules done clear
  View Solution play_arrow

• question_answer123)
  Dimension of \[R\] is?                                                              [AFMC 2003; AIIMS 2005]
  A)
                          \[M{{L}^{2}}{{T}^{-1}}\]             done clear
  B)
                            \[M{{L}^{2}}{{T}^{-3}}{{A}^{-2}}\]             done clear
  C)
                          \[M{{L}^{-1}}{{T}^{-2}}\]             done clear
  D)
                            None of these done clear
  View Solution play_arrow

• question_answer124)
  The dimensional formula of relative density is?                                                [CPMT 2003]
  A)
                          \[M{{L}^{-3}}\]                   done clear
  B)
                          \[L{{T}^{-1}}\]           done clear
  C)
                          \[ML{{T}^{-2}}\]             done clear
  D)
                          Dimensionless             done clear
  View Solution play_arrow

• question_answer125)
  The dimensional formula for young's modulus is?                                            [BHU 2003; CPMT 2004]            
  A)
                          \[M{{L}^{-1}}{{T}^{-2}}\]             done clear
  B)
                          \[{{M}^{0}}L{{T}^{-2}}\]             done clear
  C)
                          \[ML{{T}^{-2}}\]             done clear
  D)
                            \[M{{L}^{2}}{{T}^{-2}}\] done clear
  View Solution play_arrow

• question_answer126)
  Frequency is the function of density \[(\rho )\], length \[(a)\] and surface tension \[(T)\]. Then its value is?             [BHU 2003]            
  A)
                          \[k{{\rho }^{1/2}}{{a}^{3/2}}\mathbf{/}\sqrt{T}\]             done clear
  B)
                            \[k{{\rho }^{3/2}}{{a}^{3/2}}/\sqrt{T}\]             done clear
  C)
                          \[k{{\rho }^{1/2}}{{a}^{3/2}}/{{T}^{3/4}}\]             done clear
  D)
                          \[k{{\rho }^{1/2}}{{a}^{1/2}}/{{T}^{3/2}}\] done clear
  View Solution play_arrow

• question_answer127)
  The dimensions of electric potential are?         [UPSEAT 2003]
  A)
                          \[[M{{L}^{2}}{{T}^{-2}}{{Q}^{-1}}]\]             done clear
  B)
                            \[[ML{{T}^{-2}}{{Q}^{-1}}]\]                 done clear
  C)
                          \[[M{{L}^{2}}{{T}^{-1}}Q]\]             done clear
  D)
                            \[[M{{L}^{2}}{{T}^{-2}}Q]\] done clear
  View Solution play_arrow

• question_answer128)
  Dimensions of potential energy are?                [MP PET 2003]
  A)
                          \[ML{{T}^{-1}}\]             done clear
  B)
                            \[M{{L}^{2}}{{T}^{-2}}\]             done clear
  C)
                          \[M{{L}^{-1}}{{T}^{-2}}\]             done clear
  D)
                            \[M{{L}^{-1}}{{T}^{-1}}\] done clear
  View Solution play_arrow

• question_answer129)
  The dimension of \[\frac{R}{L}\] are?                                    [MP PET 2003]
  A)
                          \[{{T}^{2}}\]                      done clear
  B)
                          \[T\]           done clear
  C)
                          \[{{T}^{-1}}\]                    done clear
  D)
                          \[{{T}^{-2}}\] done clear
  View Solution play_arrow

• question_answer130)
  The dimensions of shear modulus are?                                                                                    [MP PMT 2004]
  A)
              \[ML{{T}^{-1}}\] done clear
  B)
                \[M{{L}^{2}}{{T}^{-2}}\] done clear
  C)
              \[M{{L}^{-1}}{{T}^{-2}}\] done clear
  D)
                \[ML{{T}^{-2}}\] done clear
  View Solution play_arrow

• question_answer131)
  Pressure gradient has the same dimension as that of?                                     [AFMC 2004]
  A)
              Velocity gradient          done clear
  B)
              Potential gradient done clear
  C)
              Energy gradient done clear
  D)
                None of these done clear
  View Solution play_arrow

• question_answer132)
  If force (F), length (L) and time (T) are assumed to be fundamental units, then the dimensional formula of the mass will be?                                                                                    [J & K CET 2004]
  A)
              \[F{{L}^{-1}}{{T}^{2}}\] done clear
  B)
                \[F{{L}^{-1}}{{T}^{-2}}\] done clear
  C)
              \[F{{L}^{-1}}{{T}^{-1}}\] done clear
  D)
                \[F{{L}^{2}}{{T}^{2}}\] done clear
  View Solution play_arrow

• question_answer133)
  The dimensions of universal gas constant is?                                                   [Pb. PET 2003]
  A)
              \[[M{{L}^{2}}{{T}^{-2}}{{\theta }^{-1}}]\] done clear
  B)
                \[[{{M}^{2}}L{{T}^{-2}}\theta ]\] done clear
  C)
              \[[M{{L}^{3}}{{T}^{-1}}{{\theta }^{-1}}]\] done clear
  D)
                None of these done clear
  View Solution play_arrow

• question_answer134)
  In the relation \[y=a\cos (\omega t-kx)\], the dimensional formula for k is?                             [BHU 2004]
  A)
              \[[{{M}^{0}}{{L}^{-1}}{{T}^{-1}}]\] done clear
  B)
                \[[{{M}^{0}}L{{T}^{-1}}]\] done clear
  C)
              \[[{{M}^{0}}{{L}^{-1}}{{T}^{0}}]\]           done clear
  D)
                \[[{{M}^{0}}LT]\] done clear
  View Solution play_arrow

• question_answer135)
   Position of a body with acceleration 'a' is given by \[x=K{{a}^{m}}{{t}^{n}},\]here t is time. Find dimension of m and n?                                                                                         [Orissa JEE 2005]
  A)
              \[m=1\], \[n=1\] done clear
  B)
                \[m=1,\ n=2\] done clear
  C)
              \[m=2,\ n=1\] done clear
  D)
                \[m=2,\ n=2\] done clear
  View Solution play_arrow

• question_answer136)
   "Pascal-Second" has dimension of?                                                                                        [AFMC 2005]
  A)
              Force   done clear
  B)
              Energy done clear
  C)
              Pressure done clear
  D)
                Coefficient of viscosity done clear
  View Solution play_arrow

• question_answer137)
   In a system of units if force (F), acceleration   and time (T) are taken as fundamental units then the dimensional formula of energy is?                                                                [BHU 2005]
  A)
              \[F{{A}^{2}}T\]       done clear
  B)
              \[FA{{T}^{2}}\] done clear
  C)
              \[{{F}^{2}}AT\]       done clear
  D)
              \[FAT\] done clear
  View Solution play_arrow

• question_answer138)
   Out of the following pair, which one does not have identical dimensions?                 [AIEEE 2005]
  A)
              Moment of inertia and moment of force done clear
  B)
              Work and torque done clear
  C)
              Angular momentum and Planck's constant done clear
  D)
              Impulse and momentum done clear
  View Solution play_arrow

• question_answer139)
  The ratio of the dimension of Planck's constant and that of moment of inertia is the dimension of? [CBSE PMT 2005]
  A)
              Frequency done clear
  B)
                Velocity done clear
  C)
              Angular momentum     done clear
  D)
              Time done clear
  View Solution play_arrow

• question_answer140)
   Which of the following group have different dimension?                                             [IIT JEE 2005]
  A)
              Potential difference, EMF, voltage done clear
  B)
              Pressure, stress, young's modulus done clear
  C)
              Heat, energy, work-done done clear
  D)
              Dipole moment, electric flux, electric field done clear
  View Solution play_arrow

• question_answer141)
  Out of following four dimensional quantities, which one quantity is to be called a dimensional constant? [KCET 2005]
  A)
              Acceleration due to gravity done clear
  B)
              Surface tension of water done clear
  C)
              Weight of a standard kilogram mass done clear
  D)
              The velocity of light in vacuum done clear
  View Solution play_arrow

• question_answer142)
   Density of a liquid in CGS system is 0.625\[g/c{{m}^{3}}\]. What is its magnitude in SI system? [J&K CET 2005]
  A)
              0.625   done clear
  B)
              0.0625 done clear
  C)
              0.00625 done clear
  D)
                625 done clear
  View Solution play_arrow