JEE Main & Advanced Physics Mathematical Tools, Units & Dimensions Question Bank

done Self Evaluation Test - Physical World, Units and Measurements Total Questions - 100

• question_answer1)
  In a new system of units, the fundamental quantities mass, length and time are replaced by acceleration 'a', density \['\rho '\] and frequency\[f\]. The dimensional formula for force in this system is
  A)
  \[[\rho {{a}^{4}}f]\] done clear
  B)
   \[[\rho {{a}^{4}}{{f}^{-6}}]\] done clear
  C)
   \[[{{\rho }^{-1}}{{a}^{-4}}{{f}^{6}}]\] done clear
  D)
   \[[{{\rho }^{-1}}{{a}^{-4}}{{f}^{6}}]\] done clear
  View Solution play_arrow

• question_answer2)
  When two quantities are divided, the relative error in the result is given by
  A)
  The product of the relative error in the individual quantities done clear
  B)
   The quotient of the relative error in the individual quantities done clear
  C)
   The difference of the relative error in the individual quantities done clear
  D)
   The sum of the relative error in the individual quantities done clear
  View Solution play_arrow

• question_answer3)
  The momentum of an electron in an orbit is \[h/\lambda \] where A is a constant and \[\lambda \]f is wavelength associated with it. The nuclear magneton of electron of charge e and mass \[{{m}_{e}}\]is given as \[{{\mu }_{n}}\] \[=\frac{eh}{3672\pi {{m}_{e}}}\].The dimensions of \[{{\mu }_{n}}\] are \[(A\to current)\]
  A)
  \[[M{{L}^{2}}A]\] done clear
  B)
   \[[M{{L}^{3}}A]\] done clear
  C)
   \[[{{L}^{2}}A]\] done clear
  D)
   \[[M{{L}^{2}}]\] done clear
  View Solution play_arrow

• question_answer4)
  If \[Z={{A}^{3}}\], then \[\frac{\Delta Z}{Z}=\_\_\_\_\]
  A)
  \[\frac{\Delta {{A}^{3}}}{A}\] done clear
  B)
   \[{{\left( \frac{\Delta {{A}^{{}}}}{A} \right)}^{3}}\] done clear
  C)
   \[3\left( \frac{\Delta {{A}^{{}}}}{A} \right)\] done clear
  D)
   \[{{\left( \frac{\Delta {{A}^{{}}}}{A} \right)}^{1/3}}\] done clear
  View Solution play_arrow

• question_answer5)
  The pitch and the number of circular scale divisions in a screw gauge with least count 0.02 mm are respectively
  A)
  1mm and 100 done clear
  B)
   0.5 mm and 50 done clear
  C)
   1 mm and 50 done clear
  D)
   0.5 mm and 100 done clear
  View Solution play_arrow

• question_answer6)
  If \[L=2.331cm,\,\,B=2.1cm,\]then \[L+B=\]
  A)
  4.4cm               done clear
  B)
   4cm done clear
  C)
   4.43cm             done clear
  D)
   4.431cm done clear
  View Solution play_arrow

• question_answer7)
  What is the correct number of significant figures in 0.0003026?
  A)
  Four done clear
  B)
   Seven done clear
  C)
   Eight done clear
  D)
   Six done clear
  View Solution play_arrow

• question_answer8)
  Number of significant figures in expression \[\frac{4.327g}{2.51\,c{{m}^{3}}}\] is
  A)
  2 done clear
  B)
   4      done clear
  C)
   3 done clear
  D)
   5 done clear
  View Solution play_arrow

• question_answer9)
  Error in the measurement of radius of a sphere is 1 %. Then error in the measurement of volume is
  A)
  1% done clear
  B)
   5%   done clear
  C)
   3% done clear
  D)
   8% done clear
  View Solution play_arrow

• question_answer10)
  In order to measure physical quantities in the sub-atomic world, the quantum theory often employs energy [E], angular momentum [J] and velocity [c] as fundamental dimensions instead of the usual mass, length and time. Then, the dimension of pressure in this theory is
  A)
  \[\frac{{{[E]}^{4}}}{{{[J]}^{3}}{{[c]}^{3}}}\] done clear
  B)
   \[\frac{{{[E]}^{2}}}{[J][c]}\] done clear
  C)
   \[\frac{[E]}{{{[J]}^{2}}{{[c]}^{2}}}\] done clear
  D)
   \[\frac{{{[E]}^{3}}}{{{[J]}^{2}}{{[c]}^{2}}}\] done clear
  View Solution play_arrow

• question_answer11)
  In equation\[r={{m}^{2}}sin\pi t\] , where t represents time. If the unit of m is N, then the unit of r is
  A)
  N done clear
  B)
  \[{{N}^{2}}\]   done clear
  C)
   Ns done clear
  D)
   \[{{N}^{2}}s\] done clear
  View Solution play_arrow

• question_answer12)
  If \[x=at+b{{t}^{2}}\], where x is the distance travelled by the body in kilometers while t is the time in seconds, then the unit of & is
  A)
  km/s done clear
  B)
   \[kms\] done clear
  C)
   \[km/{{s}^{2}}\] done clear
  D)
   \[km{{s}^{2}}\] done clear
  View Solution play_arrow

• question_answer13)
  The electric field is given by \[\overset{\to }{\mathop{E}}\,=\frac{A}{{{x}^{3}}}\hat{i}+By\hat{j}+C{{z}^{2}}\hat{k}\].The SI units of A, B and C are respectively: [where x, y and z are in m]
  A)
  \[\frac{N-{{m}^{3}}}{{{x}^{3}}},V/{{m}^{2}},\,N/{{m}^{2}}-C\] done clear
  B)
   \[V-{{m}^{2}},V/m,\,N/{{m}^{2}}-C\] done clear
  C)
   \[V/{{m}^{2}},V/m,\,N-C/{{m}^{2}}\] done clear
  D)
   \[V/m,\,N-{{m}^{3}}/C,\,N-C/m\] done clear
  View Solution play_arrow

• question_answer14)
  If unit of length and force are increased 4 times. The unit of energy
  A)
  Is increased by 4 times done clear
  B)
   Is increased by 16 times done clear
  C)
   Is increased by 8 times done clear
  D)
   Remains unchanged done clear
  View Solution play_arrow

• question_answer15)
  The density of a material in CGS system of unit is\[4g/c{{m}^{3}}\]. In a system of units in which unit of length is 10 cm and unit of mass is 100 g, the value of density of material will be
  A)
  0.4 done clear
  B)
   40   done clear
  C)
   400 done clear
  D)
   0.04 done clear
  View Solution play_arrow

• question_answer16)
  Young's modulus of steel is\[1.9\times {{10}^{11}}\,N/{{m}^{2}}\]. When expressed in CGS units of \[ne/c{{m}^{2}}\], it will be equal to (\[(1N={{10}^{5}}\,dyne,\,1{{m}^{2}}\,={{10}^{4}}c{{m}^{2}})\]
  A)
   \[1.9\times {{10}^{10}}\] done clear
  B)
   \[1.9\times {{10}^{11}}\] done clear
  C)
   \[1.9\times {{10}^{12}}\] done clear
  D)
   \[1.9\times {{10}^{13}}\] done clear
  View Solution play_arrow

• question_answer17)
  The speed of light in vacuum, c, depends on two fundamental constants, the permeability of free space, \[{{\mu }_{0}}\] d me permittivity of free space,\[{{\varepsilon }_{0}}.\] The speed of light is given by\[c=\frac{1}{\sqrt{{{\mu }_{0}}{{\varepsilon }_{0}}}}\]. The units of \[{{\varepsilon }_{0}}\] are \[{{N}^{-1}}{{C}^{2}}{{m}^{-2}}\]. The units for \[{{\mu }_{0}}\] are
  A)
   \[k{{g}^{-1}}{{m}^{-1}}{{C}^{2}}\] done clear
  B)
   \[kgm{{C}^{-2}}\] done clear
  C)
   \[kg\,m{{s}^{-4}}{{C}^{-2}}\] done clear
  D)
   \[k{{g}^{-1}}{{s}^{-3}}{{C}^{-2}}\] done clear
  View Solution play_arrow

• question_answer18)
  Which of the following quantities has not been expressed in proper unit?
  A)
   Torque, newton metre done clear
  B)
   Stress, newton \[metr{{e}^{-2}}\] done clear
  C)
   Modulus of elasticity, newton \[metr{{e}^{-2}}\] done clear
  D)
   Surface tension, newton \[metr{{e}^{-2}}\] done clear
  View Solution play_arrow

• question_answer19)
  E, m, J and G denote energy, mass, angular momentum and gravitational constant respectively, then the unit of \[\frac{E{{J}^{2}}}{{{m}^{5}}{{G}^{2}}}\]is
  A)
   Newton done clear
  B)
   metre done clear
  C)
   Kilogram done clear
  D)
   unitless done clear
  View Solution play_arrow

• question_answer20)
  In a certain system of units, 1 unit of time is 5 sec, 1 unit of mass is 20 kg and 1 unit of length is 10m. In this system, one unit of power will correspond to-
  A)
   16 watts done clear
  B)
   \[\frac{1}{16}\]watts done clear
  C)
   25 watts done clear
  D)
   \[\frac{1}{25}\]watts done clear
  View Solution play_arrow

• question_answer21)
  The moment of inertia of a body rotating about a given axis is \[6.0\text{ }kg\text{ }{{m}^{2}}\]in the SI system. What is the value of the moment of inertia in a system of units in which the unit of length is 5 cm and the unit of mass is 10 g?  
  A)
   \[2.4\times {{10}^{3}}\] done clear
  B)
   \[2.4\times {{10}^{5}}\] done clear
  C)
   \[6.0\times {{10}^{3}}\] done clear
  D)
   \[6.0\times {{10}^{5}}\] done clear
  View Solution play_arrow

• question_answer22)
  The dimensional formula for relative density is
  A)
   \[[M{{L}^{-3}}]\]  done clear
  B)
   \[[{{M}^{o}}{{L}^{-3}}]\] done clear
  C)
   \[[{{M}^{o}}{{L}^{o}}{{T}^{-1}}]\] done clear
  D)
   \[[{{M}^{o}}{{L}^{o}}{{T}^{o}}]\] done clear
  View Solution play_arrow

• question_answer23)
  The dimensions of speed and velocity are
  A)
   \[[{{L}^{2}}T],[L{{T}^{-1}}]\]  done clear
  B)
   \[[L{{T}^{-1}}],[L{{T}^{-2}}]\] done clear
  C)
   \[[LT],\,[LT]\] done clear
  D)
   \[[L{{T}^{-1}}],[L{{T}^{-1}}]\] done clear
  View Solution play_arrow

• question_answer24)
  \[[ML{{T}^{-1}}]+[ML{{T}^{-1}}]=..........\]
  A)
   \[[{{M}^{o}}{{L}^{o}}{{T}^{o}}]\]  done clear
  B)
   \[[ML{{T}^{-1}}]\] done clear
  C)
    \[2[ML{{T}^{-1}}]\] done clear
  D)
   None of these done clear
  View Solution play_arrow

• question_answer25)
  The physical quantity that has no dimensions is
  A)
   Strain  done clear
  B)
   angular velocity done clear
  C)
   Angular momentum done clear
  D)
   linear momentum done clear
  View Solution play_arrow

• question_answer26)
  Dimensions of specific heat are
  A)
   \[[M{{L}^{2}}{{T}^{-2}}K]\] done clear
  B)
   \[[M{{L}^{2}}{{T}^{-2}}{{K}^{-1}}]\] done clear
  C)
   \[[M{{L}^{2}}{{T}^{2}}{{K}^{-1}}]\] done clear
  D)
   \[[{{L}^{2}}{{T}^{-2}}{{K}^{-1}}]\] done clear
  View Solution play_arrow

• question_answer27)
  The dimensions of coefficient of self-inductance are
  A)
  \[[M{{L}^{2}}{{T}^{-2}}{{A}^{-2]}}]\] done clear
  B)
   \[[M{{L}^{2}}{{T}^{-2}}{{A}^{-1}}]\] done clear
  C)
   \[[ML{{T}^{-2}}{{A}^{-2}}]\] done clear
  D)
   \[[ML{{T}^{-2}}{{A}^{-1}}]\] done clear
  View Solution play_arrow

• question_answer28)
  The division of energy by time is X. The dimensional formula of X is same as that of
  A)
   Momentum done clear
  B)
   power done clear
  C)
   Torque  done clear
  D)
   electric field done clear
  View Solution play_arrow

• question_answer29)
  Which of the following is a dimensional constant?
  A)
   Refractive index   done clear
  B)
   Dielectric constant done clear
  C)
   Relative density done clear
  D)
      Gravitational constant done clear
  View Solution play_arrow

• question_answer30)
  Which one of the following represents the correct dimensions of the coefficient of viscosity?
  A)
   \[[M{{L}^{-1}}{{T}^{-1}}]\] done clear
  B)
   \[[ML{{T}^{-1}}]\] done clear
  C)
   \[[M{{L}^{-1}}{{T}^{-2}}]\] done clear
  D)
   \[[M{{L}^{-2}}{{T}^{-2}}]\] done clear
  View Solution play_arrow

• question_answer31)
  The ratio of the dimensions of Planck's constant and that of the moment of inertia is the dimensions of
  A)
  Time  done clear
  B)
  frequency done clear
  C)
  Angular momentum done clear
  D)
  velocity done clear
  View Solution play_arrow

• question_answer32)
  Two quantities A and B have same dimensions which mathematical operation given below is physically meaningful?
  A)
   \[A/B\] done clear
  B)
   \[A+{{B}^{2}}\] done clear
  C)
   \[{{A}^{2}}-B\] done clear
  D)
   \[A={{B}^{2}}\] done clear
  View Solution play_arrow

• question_answer33)
  The solar constant is defined as the energy incident per unit area per second. The dimensional formula for solar constant is
  A)
   \[[{{M}^{0}}{{L}^{0}}{{T}^{0}}]\] done clear
  B)
     \[[ML{{T}^{-2}}]\] done clear
  C)
   \[[M{{L}^{2}}{{T}^{-2}}]\] done clear
  D)
   \[[M{{L}^{0}}{{T}^{-3}}]\] done clear
  View Solution play_arrow

• question_answer34)
  Distance travelled by a particle at any instant ?t? can be represented as \[S=A(t+B)+C{{t}^{2}}\].The dimensions of B are
  A)
         \[[{{M}^{0}}{{L}^{1}}{{T}^{-1}}]\] done clear
  B)
   \[[{{M}^{0}}{{L}^{0}}{{T}^{1}}]\] done clear
  C)
   \[[{{M}^{0}}{{L}^{-1}}{{T}^{-2}}]\] done clear
  D)
   \[[{{M}^{0}}{{L}^{2}}{{T}^{-2}}]\] done clear
  View Solution play_arrow

• question_answer35)
  If P, Q, R are physical quantities, having different dimensions, which of the following combinations can never be a meaningful quantity?
  A)
   \[(P-Q)/R\] done clear
  B)
   \[PQ-R\] done clear
  C)
   \[PQ/R\] done clear
  D)
  \[(PQ-{{Q}^{2}})/R\] done clear
  View Solution play_arrow

• question_answer36)
  Dimensions of 'resistance' are same as (where h is Planck's constant and e is charge)
  A)
   \[\frac{h}{e}\] done clear
  B)
   \[\frac{{{h}^{2}}}{e}\] done clear
  C)
   \[\frac{h}{{{e}^{2}}}\] done clear
  D)
   \[\frac{{{h}^{2}}}{{{e}^{2}}}\] done clear
  View Solution play_arrow

• question_answer37)
  If \[v=\frac{a}{t}+b{{t}^{3}}\] where \[v=\]velocity and t is time The dimensional formula of a and b are
  A)
   \[[T],\,[{{T}^{-3}}]\] done clear
  B)
     \[[L],\,[L{{T}^{-4}}]\] done clear
  C)
   \[[{{T}^{-3}}],[T]\] done clear
  D)
   \[[L{{T}^{-4}}],[L]\] done clear
  View Solution play_arrow

• question_answer38)
  The displacement of a body at a particular second n is given by the expression \[{{S}_{nth}}=u+\frac{a}{2}(2n-1)\]. The dimensional formula of \[{{S}_{nth}}\] in this equation is   
  A)
     \[[{{M}^{1}}{{L}^{0}}{{T}^{1}}]\] done clear
  B)
     \[[{{M}^{0}}{{L}^{1}}{{T}^{0}}]\] done clear
  C)
   \[[{{M}^{0}}{{L}^{1}}{{T}^{-1}}]\]  done clear
  D)
   \[[{{M}^{0}}{{L}^{0}}{{T}^{0}}]\] done clear
  View Solution play_arrow

• question_answer39)
  In the equation\[P=\frac{RT}{V-b}{{e}^{\frac{aV}{RT}}}\] \[V=\]Volume, \[P=\]Pressure, \[R=\]universal gas constant, and \[T=\]temperature The dimensional formula of a is same as that of
  A)
   V  done clear
  B)
   P   done clear
  C)
   T  done clear
  D)
   R done clear
  View Solution play_arrow

• question_answer40)
  Let Q denote the charge on the plate of a capacitor of capacitance C. The dimensional formula for \[\frac{{{Q}^{2}}}{C}\]is
  A)
   \[[{{L}^{2}}{{M}^{2}}T]\] done clear
  B)
      \[[LM{{T}^{2}}]\] done clear
  C)
   \[[{{L}^{2}}M{{T}^{-2}}]\] done clear
  D)
   \[[{{L}^{2}}{{M}^{2}}{{T}^{2}}]\] done clear
  View Solution play_arrow

• question_answer41)
  Suppose the kinetic energy of a body oscillating with amplitude A and at a distance x is given by \[K=\frac{Bx}{{{x}^{2}}+{{A}^{2}}}\] The dimensions of B are the same as that of
  A)
   work/time done clear
  B)
   work x distance done clear
  C)
   work/distance done clear
  D)
   work x time done clear
  View Solution play_arrow

• question_answer42)
  If the dimensions of a physical quantity are given by \[{{M}^{a}}{{L}^{b}}{{T}^{c}}\], then the physical quantity will be
  A)
   Velocity if \[a=1,\text{ }b=0,\text{ }c=-1\] done clear
  B)
   Acceleration if \[a=1,\text{ }b=1,\text{ }c=-2\] done clear
  C)
   Force if \[a=0,\text{ }b=-1,\text{ }c=-2\] done clear
  D)
   Pressure if \[a=1,\text{ }b=-1,\text{ }c=-2\] done clear
  View Solution play_arrow

• question_answer43)
  Which one of the following represents the correct dimensions of the gravitational constant?
  A)
   \[[{{M}^{-1}}{{L}^{3}}{{T}^{-2}}]\] done clear
  B)
   \[[ML{{T}^{-1}}]\] done clear
  C)
  done clear
  D)
   \[[M{{L}^{-2}}{{T}^{-2}}]\] done clear
  View Solution play_arrow

• question_answer44)
  Write the dimensions of \[a\times b\]in the relation \[E=\frac{b-{{x}^{2}}}{at}\]where E is the energy, x is the displacement and t is time
  A)
   \[M{{L}^{2}}T\]  done clear
  B)
   \[{{M}^{-1}}{{L}^{2}}{{T}^{1}}\] done clear
  C)
   \[M{{L}^{2}}{{T}^{-2}}\] done clear
  D)
   \[ML{{T}^{-2}}\] done clear
  View Solution play_arrow

• question_answer45)
  The dimensions of the quantity \[\overset{\to }{\mathop{E}}\,\times \overset{\to }{\mathop{B}}\,\]where\[\overset{\to }{\mathop{E}}\,\] represents the electric field and \[\overset{\to }{\mathop{B}}\,\] the magnetic field may be given as:
  A)
   \[[M{{L}^{3}}]\] done clear
  B)
   \[[{{M}^{2}}L{{T}^{-5}}{{A}^{-2}}]\] done clear
  C)
   \[[{{M}^{2}}{{L}^{-3}}{{T}^{2}}{{A}^{-1}}]\] done clear
  D)
   \[[ML{{T}^{-2}}{{A}^{-2}}]\] done clear
  View Solution play_arrow

• question_answer46)
  What are the dimensions of A/B in the relation \[F=A\sqrt{x}+B{{t}^{2}}\], where F is the force, x is the distance and t is time?
  A)
   \[M{{L}^{2}}{{T}^{-2}}\] done clear
  B)
   \[{{L}^{-1/2}}{{T}^{2}}\] done clear
  C)
   \[{{L}^{-1/2}}{{T}^{-1}}\] done clear
  D)
   \[L{{T}^{-2}}\] done clear
  View Solution play_arrow

• question_answer47)
  A physical quantity x depends on quantities y and z as follows: \[x=Ay+B\text{ }tan\text{ }Cz\], where A, B and C are constants. Which of the following do not have the same dimensions :
  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_answer48)
  A quantity X is given by \[{{\varepsilon }_{0}}L\frac{\Delta V}{\Delta t}\] where \[{{\in }_{0}}\] is the permittivity of the free space, L is a length, \[\Delta V\]is a potential difference and \[\Delta t\] is a time interval. The dimensional formula for X is the same as that of        
  A)
             Resistance  done clear
  B)
   charge done clear
  C)
   Voltage  done clear
  D)
   current done clear
  View Solution play_arrow

• question_answer49)
  The thrust developed by a rocket-motor is given by \[F=mv+A({{P}_{1}}-{{P}_{2}})\] where m is the mass of the gas ejected per unit time, v is velocity of the gas, A is area of cross-section of the nozzle, \[{{P}_{1}}\] and \[{{P}_{2}}\] are the pressures of the exhaust gas and surrounding atmosphere. The formula dimensionally
  A)
   Correct done clear
  B)
   Wrong done clear
  C)
   Sometimes wrong, sometimes correct done clear
  D)
   Data is not adequate done clear
  View Solution play_arrow

• question_answer50)
  A, B, C and D are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation \[AD=C\text{ }In\text{ (}BD\text{)}\]holds true. Then which of the combination is not a meaningful quantity?
  A)
   \[\frac{C}{BD}-\frac{A{{D}^{2}}}{C}\] done clear
  B)
   \[{{A}^{2}}-{{B}^{2}}{{C}^{2}}\] done clear
  C)
   \[\frac{A}{B}-C\] done clear
  D)
   \[\frac{(A-C)}{D}\] done clear
  View Solution play_arrow

• question_answer51)
    If electronic charge e, electron mass m, speed of light in vacuum c and Planck's constant h are taken as fundamental quantities, the permeability of vacuum \[{{\mu }_{0}}\] can be expressed in units of      
  A)
             \[\left( \frac{h}{m{{e}^{2}}} \right)\] done clear
  B)
   \[\left( \frac{hc}{m{{e}^{2}}} \right)\] done clear
  C)
   \[\left( \frac{h}{c{{e}^{2}}} \right)\] done clear
  D)
   \[\left( \frac{m{{c}^{2}}}{h{{e}^{2}}} \right)\] done clear
  View Solution play_arrow

• question_answer52)
   A boy recalls the relation almost correctly but for gets where to put the constant c (speed of light). He writes; \[m=\frac{{{m}_{0}}}{\sqrt{1-{{v}^{2}}}}\], where m and \[{{m}_{0}}\] stand  masses and v for speed. Right place of c is
  A)
  \[m=\frac{c{{m}_{0}}}{\sqrt{1-{{v}^{2}}}}\] done clear
  B)
   \[m=\frac{{{m}_{0}}}{c\sqrt{1-{{v}^{2}}}}\] done clear
  C)
   \[m=\frac{{{m}_{0}}}{\sqrt{{{c}^{2}}-{{v}^{2}}}}\] done clear
  D)
   \[m=\frac{{{m}_{0}}}{\sqrt{1-\frac{{{v}^{2}}}{{{c}^{2}}}}}\] done clear
  View Solution play_arrow

• question_answer53)
  When a small sphere moves at low speed through a fluid, the viscous force F, opposing the motion is experimentally found to depend upon the radius r, the velocity v of the sphere and the viscosity \[\eta \] of the fluid. Expression for force is
  A)
  \[4\pi \eta r{{v}^{2}}\] done clear
  B)
   \[4\pi \eta {{r}^{2}}v\] done clear
  C)
   \[2\pi \eta {{r}^{2}}v\] done clear
  D)
   \[6\pi \eta rv\] done clear
  View Solution play_arrow

• question_answer54)
  With the usual notations, the following equation \[{{S}_{t}}=u+\frac{1}{2}a(2t-1)\]is
  A)
  Only numerically correct done clear
  B)
   Only dimensionally correct done clear
  C)
   Both numerically and dimensionally correct done clear
  D)
   Neither numerically nor dimensionally correct done clear
  View Solution play_arrow

• question_answer55)
  Dimensionally wavelength is equivalent to
  A)
  \[\frac{E\sqrt{LC}}{B}\] done clear
  B)
   \[\frac{E}{B\sqrt{LC}}\] done clear
  C)
   \[\frac{B\sqrt{LC}}{E}\] done clear
  D)
   \[\frac{B}{E\sqrt{LC}}\] done clear
  View Solution play_arrow

• question_answer56)
  If velocity (V), force (F) and energy (E) are taken as fundamental units, then dimensional formula for mass will be
  A)
  \[{{V}^{-2}}{{F}^{0}}{{E}^{3}}\] done clear
  B)
   \[{{V}^{0}}F{{E}^{2}}\] done clear
  C)
   \[V{{F}^{-2}}{{E}^{0}}\] done clear
  D)
   \[{{V}^{-2}}{{F}^{0}}E\] done clear
  View Solution play_arrow

• question_answer57)
    The period of a body under SHM is represented 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.
  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
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• question_answer58)
  A physical quantity of the dimensions of length that can be formed out of c, G and \[\frac{{{e}^{2}}}{4\pi {{\varepsilon }_{0}}}\] is [c is velocity of light, G is universal constant of gravitation and e is charge]  
  A)
  \[{{c}^{2}}\left[ G\frac{{{e}^{2}}}{4\pi {{\varepsilon }_{0}}} \right]\] done clear
  B)
   \[\frac{1}{{{c}^{2}}}{{\left[ \frac{{{e}^{2}}}{G4\pi {{\varepsilon }_{0}}} \right]}^{1/2}}\] done clear
  C)
   \[\frac{1}{c}G\frac{{{e}^{2}}}{4\pi {{\varepsilon }_{0}}}\] done clear
  D)
   \[\frac{1}{{{c}^{2}}}{{\left[ G\frac{{{e}^{2}}}{4\pi {{\varepsilon }_{0}}} \right]}^{1/2}}\] done clear
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• question_answer59)
  Assuming that the mass m of the largest stone that can be moved by a flowing river depends upon the velocity v of the water, its density \[\rho \] and the acceleration due to gravity g. Then m is directly proportional to:
  A)
  \[{{\nu }^{3}}\] done clear
  B)
   \[{{\nu }^{4}}\] done clear
  C)
   \[{{\nu }^{5}}\] done clear
  D)
   \[{{\nu }^{6}}\] done clear
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• question_answer60)
  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:
  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 these done clear
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• question_answer61)
  If x and R stands for distance. Then which of the following is dimensionally same as\[\int{\frac{Rdx}{{{x}^{2}}}}\]?
  A)
  \[R{{x}^{2}}\] done clear
  B)
   \[2xR\] done clear
  C)
   \[\frac{R}{x}\] done clear
  D)
   \[-\frac{{{R}^{2}}}{x}\]   done clear
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• question_answer62)
  The unit of the coefficient of viscosity in S.I. system is
  A)
  m/kg-s done clear
  B)
   \[m-s/k{{g}^{2}}\] done clear
  C)
   \[kg/m-{{s}^{2}}\] done clear
  D)
   kg/m-s done clear
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• question_answer63)
  The unit of the Stefan-Boltzmann's constant is
  A)
  \[W/{{m}^{2}}{{k}^{4}}\] done clear
  B)
   \[W/{{m}^{2}}\] done clear
  C)
   \[W/{{m}^{2}}K\] done clear
  D)
   \[W/{{m}^{2}}{{K}^{2}}\] done clear
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• question_answer64)
  Unit of specific resistance is
  A)
  \[ohm/{{m}^{2}}\] done clear
  B)
   \[ohm/{{m}^{3}}\] done clear
  C)
   \[ohm-m\] done clear
  D)
   \[ohm/m\] done clear
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• question_answer65)
  Unit of magnetic moment is
  A)
  ampere-\[metr{{e}^{2}}\] done clear
  B)
   ampere-metre done clear
  C)
   weber-\[metr{{e}^{2}}\] done clear
  D)
   weber/metre done clear
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• question_answer66)
  Surface tension of a liquid is 70 dyne/cm. Its value in SI is
  A)
  \[70N/m\] done clear
  B)
   \[7\times {{10}^{-2}}N/m\] done clear
  C)
   \[7\times {{10}^{2}}N/m\] done clear
  D)
   \[7\times {{10}^{3}}N/m\] done clear
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• question_answer67)
  Which of the following represents incorrect unit?
  A)
  Pressure \[=N{{m}^{2}}\] done clear
  B)
          Surface tension \[=N/m\] done clear
  C)
   \[Energy=kg-m/sec\] done clear
  D)
   \[\frac{Stress}{Strain}=N/{{m}^{2}}\] done clear
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• question_answer68)
  Which one of the following is not measured in units of energy?         
  A)
  Couple x angle    done clear
  B)
        Moment of inertia \[\times {{(angular\text{ }velocity)}^{2}}\] done clear
  C)
   \[Force~\,\times \,distance\] done clear
  D)
   \[Impulse\,\times \,time\] done clear
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• question_answer69)
  The numerical values of young's modulus in S.I. unit is \[\beta \]. What is its numerical value in \[cgs\] system?
  A)
  \[\beta \] done clear
  B)
   10\[\beta \]   done clear
  C)
   \[\beta \]/10 done clear
  D)
   100\[\beta \] done clear
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• question_answer70)
  In the eqn.\[\left( P+\frac{a}{{{V}^{2}}} \right)(v-b)=cons\text{tant}\], the Unit of a is  
  A)
  \[dyne\times c{{m}^{5}}\]    done clear
  B)
          \[dyne\times c{{m}^{4}}\] done clear
  C)
   \[dyne/c{{m}^{3}}\]      done clear
  D)
          \[dyne\times c{{m}^{2}}\] done clear
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• question_answer71)
  The value of resistance is \[10.845\Omega \] and the value of current is 3.23 A. The potential difference is 35.02935 volt. Its value in significant number would be
  A)
  35V done clear
  B)
   35.0V done clear
  C)
   35.03V done clear
  D)
   35.029V done clear
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• question_answer72)
  Which of the following statements is/are correct?

  I. 345.726 has six significant figures.

  II. 0.004289 has seven significant figures.

  III. 125000 has three significant figures.

  IV. 9.0042 has five significant figures.

  A)
  I only done clear
  B)
   II only done clear
  C)
   I, III and IV done clear
  D)
   II, III and IV done clear
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• question_answer73)
  Resistance \[R=V/I\], here \[V=(100\pm 5)\text{ }V\]and\[I=(10\pm 0.2)\text{ }A\]. Find percentage error in R.
  A)
  5% done clear
  B)
   2%   done clear
  C)
   7% done clear
  D)
   3% done clear
  View Solution play_arrow

• question_answer74)
  A wire has a mass \[0.3\pm 0.003\text{ }g\], radius \[0.5\pm 0.005\text{ }mm\] and length \[6\pm 0.06\text{ }on\]. The maximum percentage error in the measurement of its density is
  A)
  1 done clear
  B)
   2     done clear
  C)
   3 done clear
  D)
   4 done clear
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• question_answer75)
  The pitch of the screw gauge is 0.5 mm. Its circular scale contains 50 divisions. The least count of the screw gauge is
  A)
  0.001mm done clear
  B)
   0.01mm done clear
  C)
   0.02mm done clear
  D)
   0.025mm done clear
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• question_answer76)
  In a vernier callipers N division of vernier coincide with \[(N-1)\] divisions of main scale in which length of a division is 1 mm. The least count of the instrument in cm is
  A)
  N done clear
  B)
   \[N-1\]  done clear
  C)
   \[\frac{1}{10N}\] done clear
  D)
   \[(1/N)-1\] done clear
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• question_answer77)
  One centimeter on the main scale of a vernier calipers is divided into 10 equal parts. If 10 divisions of vernier coincide with 8 small divisions of the main scale, the least count of vernier calipers  is
  A)
  0.01 cm done clear
  B)
   0.02 cm done clear
  C)
   0.05 cm done clear
  D)
   0.005 cm done clear
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• question_answer78)
  Relative density of a metal may be found with the help of spring balance. In air the spring balance reads \[(5.00~\,\,\pm \,\,0.05)\text{ }N\]and in water it reads\[\text{(}4.00\,\,\pm \,\,0.05\text{) }N\]. Then, the relative density along with the maximum permissible percentage error would be
  A)
  \[(5.00\,\,\pm \,\,0.05)\] done clear
  B)
   \[(5.00\,\,\pm \,\,11%)\] done clear
  C)
  \[(5.00\,\,\pm \,\,0.10)\] done clear
  D)
   \[(5.00\,\,\pm \,\,6%)\] done clear
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• question_answer79)
  The refractive index of water measured by the relation \[\mu =\frac{real\,depth}{apparent\,\operatorname{depth}}\]is found to have values of 1.34,1.38,1.32 and 1.36; the mean value of refractive index with percentage error is
  A)
  \[1.35\,\,\pm \,\,1.48%\] done clear
  B)
  \[1.35\,\,\pm \,\,0%\] done clear
  C)
   \[1.36\,\,\pm \,\,6%\] done clear
  D)
   \[1.36\,\,\pm \,\,0%\] done clear
  View Solution play_arrow

• question_answer80)
  In an experiment four quantities a, b, c and d are measured with percentage error 1%, 2%, 3% and 4% respectively. Quantity P is calculated as follows \[P=\frac{{{a}^{3}}{{b}^{2}}}{cd}%\] error in P is
  A)
  10% done clear
  B)
   7%   done clear
  C)
   4% done clear
  D)
   14% done clear
  View Solution play_arrow

• question_answer81)
  The heat generated in a circuit is given by\[Q={{I}^{2}}Rt\], where I is current, R is resistance and t is time. If the percentage errors in measuring I, R and t are 2%, 1% and 1% respectively, then the maximum error in measuring heat will be
  A)
  2% done clear
  B)
   3%   done clear
  C)
   4% done clear
  D)
   6% done clear
  View Solution play_arrow

• question_answer82)
  The pressure on a square plate is measured by measuring the force on the plate and length of the sides of the plate by using the formula \[P=\frac{F}{{{\ell }^{2}}}\]. If the maximum errors in the measurement of force and length are 6% and 3% respectively, then the maximum error in the measurement of pressure is          
  A)
  1% done clear
  B)
   2%   done clear
  C)
   12% done clear
  D)
   10% done clear
  View Solution play_arrow

• question_answer83)
  An atomic clock has an accuracy of 1 part is \[{{10}^{10}}\] If two such clocks are operated with precision, then after running for 2500 years these will record a difference of nearly.
  A)
  1 sec     done clear
  B)
   8 sec done clear
  C)
   5 sec    done clear
  D)
   10 sec done clear
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• question_answer84)
  Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are 3% each, then error in the value of resistance of the wire is
  A)
  6% done clear
  B)
   zero     done clear
  C)
   1% done clear
  D)
   3%         done clear
  View Solution play_arrow

• question_answer85)
  Which of the following is most accurate?
  A)
  A screw gauge of least count 0.001 mm done clear
  B)
   A screw gauge having pitch 1 mm and 50 divisions on circular scale done clear
  C)
   A vernier callipers of least count 0.01 mm done clear
  D)
   Vernier callipers having 20 divisions on the sliding scale (vernier scale) coinciding 19 divisions on the main millimetre scale done clear
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• question_answer86)
  A thin copper wire of length / metre increases in length by 2% when heated through\[10{}^\circ C\]. What is the percentage increase in area when a square copper sheet of length / metre is heated through \[10{}^\circ C?\]
  A)
  4% done clear
  B)
   8% done clear
  C)
   16% done clear
  D)
   None of these done clear
  View Solution play_arrow

• question_answer87)
  A physical quantity \[\zeta \]is calulated using the formula\[\zeta =\frac{1}{10}x{{y}^{2}}/{{z}^{1/3}}\], where x, y and z are experimentally measured quantities. If the fractional error in the measurement of x, y and z are 2 %, 1% and 3% respectively, then the fractional error in\[\zeta \]will be
  A)
  0.5% done clear
  B)
   5%   done clear
  C)
   6% done clear
  D)
   7% done clear
  View Solution play_arrow

• question_answer88)
  In a simple pendulum experiment, the maximum percentage error in the measurement of length is 2% and that in the observation of the time- period is 3%. Then the maximum percentage error in determination of the acceleration due to gravity g is
  A)
  5% done clear
  B)
   6%   done clear
  C)
   1% done clear
  D)
   8% done clear
  View Solution play_arrow

• question_answer89)
  Area of a square is\[\text{(}100\pm 2\text{)}{{m}^{2}}\]. Its side is
  A)
  \[\text{(}10\pm 1\text{)}m\] done clear
  B)
   \[\text{(}10\pm 0.1\text{)}m\] done clear
  C)
   \[\text{(}10\pm \sqrt{2}\text{)}m\] done clear
  D)
   \[10\pm \sqrt{2}%\] done clear
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• question_answer90)
  The values of kinetic energy K and potential energy U are measured as follows: \[K=100.0\pm 2.0\text{ }J,\,\,\,U=200.0\pm 1.0\text{ }J\]. Then the percentage error in the measurement of mechanical energy is -
  A)
  2.5% done clear
  B)
   1%   done clear
  C)
   0.5% done clear
  D)
   1.5% done clear
  View Solution play_arrow

• question_answer91)
  You measure two quantities as\[A=1.0m\pm 0.2m\]\[B=2.0m\pm 0.2m\]. We should report correct value for \[\sqrt{AB}\] as
  A)
  \[1.4m\pm 0.4m\] done clear
  B)
   \[1.41m\pm 0.15m\] done clear
  C)
   \[1.4m\pm 0.3m\] done clear
  D)
   \[1.4m\pm 0.2m\] done clear
  View Solution play_arrow

• question_answer92)
  The resistance of a metal is given by \[R=\frac{V}{I}\]where V is potential difference and I is the current. In a circuit the potential difference across resistance is \[V=(8\pm 0.5)V\] and current in resistance \[I=(2\pm 0.2)A\]. What is the value of resistance with its percentage error?
  A)
  \[4\Omega \pm 16.25%\] done clear
  B)
   \[(4\pm 0.7)\Omega \] done clear
  C)
   \[4\Omega \pm 0.7%\] done clear
  D)
   \[4\Omega \pm 7%\] done clear
  View Solution play_arrow

• question_answer93)
  The density of a sphere is measured by measuring its mass and diameter. If, it is known that the maximum percentage errors in the measurement are 2% and 3%, then find the maximum percentage error in the measurement of density?
  A)
  15% done clear
  B)
   18%  done clear
  C)
   9% done clear
  D)
   11% done clear
  View Solution play_arrow

• question_answer94)
  The length of a cylinder is measured with a metre rod having least count 0.1 cm. Its diameter is measured with vernier callipers having least count cm. Given that length is 5.0 cm and radius is 2.00 cm. The percentage error in the calculated value of the volume will be:
  A)
  11% done clear
  B)
   2%   done clear
  C)
   3%  done clear
  D)
   4% done clear
  View Solution play_arrow

• question_answer95)
  Intensity observed in an interference pattern is \[I={{I}_{0}}Si{{n}^{2}}\]. \[At\theta ={{30}^{o}}\] intensity \[I=5\pm 0.0020W/{{m}^{2}}\]. Find percentage error in angle if \[{{I}_{0}}=20W/{{m}^{2}}\]                       
  A)
  \[\frac{4}{\pi }\sqrt{3}\times {{10}^{-2}}%\]    done clear
  B)
          \[\frac{2}{\pi }\sqrt{3}\times {{10}^{-2}}%\] done clear
  C)
   \[\frac{1}{\pi }\sqrt{3}\times {{10}^{-2}}%\] done clear
  D)
          \[\frac{3}{\pi }\sqrt{3}\times {{10}^{-2}}%\] done clear
  View Solution play_arrow

• question_answer96)
  The resistance R of a wire is given by the relation \[R=\frac{\rho \ell }{\pi {{r}^{2}}}\]. Percentage error in the measurement of \[\rho ,\,\,\ell \] and r is 1%, 2% and 3% respectively. Then the percentage error in the measurement of R is
  A)
  6 done clear
  B)
   9     done clear
  C)
   8 done clear
  D)
   10 done clear
  View Solution play_arrow

• question_answer97)
  A physical quantity A is related to four observable quantities a, b, c and d as follows, \[A=\frac{{{a}^{2}}{{b}^{3}}}{c\sqrt{d}}\] and the percentage errors of measurement in a, b, c and d are 1%, 3%, 2% and 2% respectively What is the percentage error in the quantity A?
  A)
  12% done clear
  B)
   7%   done clear
  C)
   5% done clear
  D)
   14% done clear
  View Solution play_arrow

• question_answer98)
  A physical quantity Q is related to four observables x, y, z and t by the relation \[Q=\frac{{{x}^{2/5}}{{z}^{3}}}{y\sqrt{t}}\]The percentage errors of measurement in x, y, z and t are 2.5%, 2%, 0.5% and 1% respectively. The percentage error in Q will be
  A)
  5% done clear
  B)
   4.5% done clear
  C)
   8% done clear
  D)
   7.75% done clear
  View Solution play_arrow

• question_answer99)
  The frequency (f) of a wire oscillating with a length \[\ell \], in p loops, under a tension T is given by \[f=\frac{P}{2\ell }\sqrt{\frac{T}{\mu }}\] where \[\mu =\] linear density of the wire. If the error made in determining length, tension and linear density be 1%, -2% and 4%, then find the percentage error in the calculated frequency              
  A)
  - 4% done clear
  B)
   - 2% done clear
  C)
   - 1% done clear
  D)
   - 5% done clear
  View Solution play_arrow

• question_answer100)
  The current voltage relation of a diode is given by\[I=({{e}^{1000V/T}}-1)mA\], where the applied voltage V is in volts and the temperature T is in degree kelvin. If a student makes an error measuring \[\pm 0.01\text{ }V\]while measuring the current of 5 mA at 300 K, what will be the error in the value of current in mA?
  A)
  0.2Ma done clear
  B)
   0.02mA done clear
  C)
   0.5mA done clear
  D)
   0.05mA   done clear
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