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

done Mock Test - Units Dimenstions and Measurment Total Questions - 25

• question_answer1)
  If \[F=\frac{v}{C\ln (xb)}\], then
  A)
  F and v denote force and velocity, the dimensions of C are [MT] done clear
  B)
  x denotes distance, the dimensions of b are [\[L_{{}}^{-1}\]] done clear
  C)
  The dimension of \[\frac{v}{C}\] never be same as F done clear
  D)
  The dimensions of x must be same as \[\frac{v}{cb}\] done clear
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• question_answer2)
  A bus travels distance \[x_{1}^{{}}\]when accelerates from rest at constant rate\[a_{2}^{{}}\]for some time and after that travels a distance\[x_{2}^{{}}\]when decelerates at a constant rate \[a_{2}^{{}}\]to come to rest. A student established a relation \[x_{1}^{{}}+x_{2}^{{}}=\frac{a_{1}^{{}}a_{2}^{{}}t_{{}}^{2}}{2(a_{1}^{{}}+a_{2}^{{}})}\] Choose the correct option(s).
  A)
  The relation is dimensionally correct done clear
  B)
  The relation is dimensionally incorrect done clear
  C)
  The relation may be dimensionally correct done clear
  D)
  None of the above done clear
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• question_answer3)
  A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is 90 s, 91 s, 95 s and 92 s. If the minimum division in the measuring clock is 1 s, then the reported mean time should be
  A)
  \[92\pm 2s\] done clear
  B)
  \[92\pm 5.0s\] done clear
  C)
  \[92\pm 1.8s\] done clear
  D)
  \[92\pm 3s\] done clear
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• question_answer4)
  If \[m,\text{ }e,\,\,{{\varepsilon }_{0}},\] h and c denote mass electron, charge of electron. Planck's constant and speed of light, respectively. The dimensions of \[\frac{me_{{}}^{4}}{\varepsilon _{0}^{2}h_{{}}^{3}c}\] are
  A)
  [\[M_{{}}^{0}L_{{}}^{0}T_{{}}^{-1}\]]                   done clear
  B)
  [\[M_{{}}^{0}L_{{}}^{-1}T_{{}}^{-1}\]] done clear
  C)
  [\[M_{{}}^{2}L_{{}}^{{}}T_{{}}^{-3}\]]     done clear
  D)
  [\[M_{{}}^{0}L_{{}}^{-1}T_{{}}^{0}\]] done clear
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• question_answer5)
  In a direct impact, loss in kinetic energy is given by \[\Delta K=\frac{M_{1}^{{}}M_{2}^{{}}}{2(M_{1}^{{}}+M_{2}^{{}})}.(V_{1}^{{}}-V_{2}^{{}})_{{}}^{2}(1-k_{{}}^{2})\] with usual notations (except k). The quantity k will have dimensional formula
  A)
  [\[M_{{}}^{0}L_{{}}^{2}T_{{}}^{-2}\]]                   done clear
  B)
  [\[M_{{}}^{{}}L_{{}}^{{}}T_{{}}^{-1}\]] done clear
  C)
  [\[M_{{}}^{0}L_{{}}^{0}T_{{}}^{0}\]]        done clear
  D)
  [\[M_{{}}^{0}L_{{}}^{{}}T_{{}}^{-1}\]] done clear
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• question_answer6)
  While measuring the acceleration due to gravity by a simple pendulum, a student makes a positive error of 1% in the length of the pendulum and a negative error of 3% in the value of time period. His percentage error in the measurement of g by the relation \[g=4\pi _{{}}^{2}(l/T_{{}}^{2})\] will be
  A)
  2%                    done clear
  B)
  4%     done clear
  C)
  7%        done clear
  D)
  10% done clear
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• question_answer7)
  Number of particles is given by \[n=-D\frac{{{n}_{2}}-{{n}_{1}}}{{{x}^{2}}-{{x}_{1}}}\] crossing a unit area perpendicular to X-axis in unit time, where\[n_{1}^{{}}\]and \[n_{2}^{{}}\] are number of particles per unit volume for the value of \[x_{{}}^{{}}\]meant to \[x_{2}^{{}}\] and \[x_{1}^{{}}\]. Find dimensions of D called as diffusion constant
  A)
  \[M_{0}^{{}}LT_{{}}^{2}\]   done clear
  B)
  \[M_{{}}^{0}L_{{}}^{2}T_{{}}^{-4}\] done clear
  C)
  \[M_{{}}^{0}L_{{}}^{{}}T_{{}}^{-3}\]       done clear
  D)
  \[M_{{}}^{0}L_{{}}^{2}T_{{}}^{-1}\] done clear
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• question_answer8)
  Experiment shows that two perfectly neutral parallel metal plates separated by a small distance d attract each other via a very weak force, known as the Casimir force. The force per unit area of the plates, F, depends only on the Planck constant h, on the speed of light c, and on d. Which of the following has the best chance of being correct for F?
  A)
  \[F=\frac{hc}{d_{{}}^{2}}\]    done clear
  B)
  \[F=\frac{hc}{d_{{}}^{4}}\] done clear
  C)
  \[F=\frac{hd_{{}}^{2}}{c}\]    done clear
  D)
  \[F=\frac{d_{{}}^{4}}{hc}\]   done clear
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• question_answer9)
  The respective number of significant figures for the numbers 23.023, 0.0003, and 2.1 x \[10_{{}}^{-3}\] are
  A)
  5, 1, 2   done clear
  B)
  5, 1, 5 done clear
  C)
  5, 5, 2   done clear
  D)
  4, 4, 2 done clear
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• question_answer10)
  The potential energy of a particle varies with distance \[\chi \] as \[U=\frac{Ax_{{}}^{1/2}}{x_{{}}^{2}+B}\] where A and B are constants. The dimensional formula for A x B is
  A)
  \[M_{{}}^{1}L_{{}}^{7/2}T_{{}}^{-2}\]      done clear
  B)
  \[M_{{}}^{1}L_{{}}^{1/2}T_{{}}^{-2}\] done clear
  C)
  \[M_{{}}^{1}L_{{}}^{5/2}T_{{}}^{-2}\]      done clear
  D)
  \[M_{{}}^{1}L_{{}}^{9/2}T_{{}}^{-2}\] done clear
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• question_answer11)
  The relative density of a material of a body is found by weighing it first in air and then in water. If the weight of the body in air is \[W_{1}^{{}}\] = \[8.00\text{ }\pm \text{ }0.05\text{ }N\]and the weight in water is \[W_{2}^{{}}\] = \[6.00\text{ }\pm \text{ }0.05\] N, then the relative density \[\rho _{r}^{{}}=W_{1}^{{}}/(W_{1}^{{}}-W_{2}^{{}})\] With the maximum permissible error is
  A)
  \[4.00\text{ }\pm 0.62\]%            done clear
  B)
  \[4.00\text{ }\pm 0.82\]% done clear
  C)
  \[4.00\text{ }\pm 3.2\]% done clear
  D)
  \[4.00\text{ }\pm 5.62\]% done clear
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• question_answer12)
  If force F, acceleration a, and time T are taken as the fundamental physical quantities, the dimensions of length on this system of units, are
  A)
  \[FAT_{{}}^{2}\]         done clear
  B)
  FAT     done clear
  C)
  FT                    done clear
  D)
  \[AT_{{}}^{2}\] done clear
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• question_answer13)
  Which of the following product of \[e,h,\mu ,G\](where \[\mu \]is the permeability) be taken so that the dimensions of the product are same as that of the speed of light?
  A)
  \[he_{{}}^{-2}\mu _{{}}^{-1}G_{{}}^{0}\] done clear
  B)
  \[h_{{}}^{2}eG_{{}}^{0}\mu \] done clear
  C)
  \[h_{{}}^{0}e_{{}}^{2}G_{{}}^{-1}\mu \]   done clear
  D)
  \[hGe_{{}}^{-2}\mu _{{}}^{0}\] done clear
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• question_answer14)
  The best method to reduce random error is
  A)
  To change the instrument used for measurement done clear
  B)
  To take help of experienced observer done clear
  C)
  To repeat the experiment many times and to take the average results done clear
  D)
  None of the above done clear
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• question_answer15)
  The position of a particle at time \[t\]is given by the relation \[x(t)=(\frac{v_{0}^{{}}}{\alpha })(1-c_{{}}^{-\alpha t})\]where \[v_{0}^{{}}\] ls a constant and a > 0. The dimensions of \[v_{0}^{{}}\] and \[\alpha \] are respectively
  A)
  \[M_{{}}^{0}L_{{}}^{1}T_{{}}^{-1}and\,T_{{}}^{-1}\]     done clear
  B)
  \[M_{{}}^{0}L_{{}}^{1}T_{{}}^{0}and\,T_{{}}^{-1}\] done clear
  C)
  \[M_{{}}^{0}L_{{}}^{1}T_{{}}^{-1}and\,LT_{{}}^{-2}\]   done clear
  D)
  \[M_{{}}^{0}L_{{}}^{1}T_{{}}^{-1}and\,LT_{{}}^{{}}\] done clear
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• question_answer16)
  A body travels uniformly a distance of\[(S+\Delta S)\] in a time \[(t\pm \Delta t)\]. What may be the condition so that body within the error limits move with a velocity \[(\frac{S}{t}\pm \frac{\Delta S}{\Delta t})\]?
  A)
  \[\frac{\Delta t}{t}+\frac{S(\Delta t)_{{}}^{2}}{(\Delta S)t_{{}}^{2}}=\pm 1\] done clear
  B)
  \[\frac{\Delta t}{t}+\frac{S\Delta t_{{}}^{{}}}{\Delta St_{{}}^{{}}}=\pm 1\] done clear
  C)
  \[\frac{\Delta t}{t}+\frac{(\Delta S)t_{{}}^{{}}}{S(\Delta t)_{{}}^{{}}}=\pm 1\]          done clear
  D)
  \[\frac{\Delta t}{t}+\frac{S_{{}}^{2}\Delta t_{{}}^{{}}}{(\Delta S)_{{}}^{2}t_{{}}^{{}}}=\pm 1\] done clear
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• question_answer17)
  Force F is given in terms of time \[t\] and distance \[x\] by F =A sin C\[t\] + B cos\[Dx\]. Then the dimensions of \[A/B\] and \[C/D\] are
  A)
  \[[M_{{}}^{0}L_{{}}^{0}T_{{}}^{0}],[M_{{}}^{0}L_{{}}^{0}T_{{}}^{-1}]\] done clear
  B)
  \[[M_{{}}^{{}}L_{{}}^{{}}T_{{}}^{-2}],[M_{{}}^{0}L_{{}}^{-1}T_{{}}^{0}]\] done clear
  C)
  \[[M_{{}}^{0}L_{{}}^{0}T_{{}}^{0}],[M_{{}}^{0}L_{{}}^{{}}T_{{}}^{-1}]\]   done clear
  D)
  \[[M_{{}}^{0}L_{{}}^{1}T_{{}}^{-1}],[M_{{}}^{0}L_{{}}^{0}T_{{}}^{0}]\] done clear
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• question_answer18)
  The dimension of \[{{e}^{2}}/4\pi {{\varepsilon }_{2}}hc,\] where \[e,{{\varepsilon }_{0}},h\]  and c are electronic charge, electric permittivity, Planck's constant and velocity of light in vacuum, respectively, is
  A)
  \[[{{M}^{0}}{{L}^{0}}{{T}^{0}}]\] done clear
  B)
  \[[{{M}^{1}}{{L}^{0}}{{T}^{0}}]\] done clear
  C)
  \[[{{M}^{0}}{{L}^{1}}{{T}^{0}}]\]             done clear
  D)
  \[[{{M}^{0}}{{L}^{0}}{{T}^{1}}]\] done clear
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• question_answer19)
  A screw gauge with a pitch of 0.5 mm and a circular scale with 50 divisions is used to measure the thickness of a thin sheet of Aluminium. Before starting the measurement, it is found that when the two jaws of the screw gauge are brought in contact, the 45th division coincides with the main scale line and that the zero of the main scale is barely visible. What is the thickness of the sheet if the main scale reading is 0.5 mm and the 25th division coincides the main scale line?
  A)
  0.75 mm           done clear
  B)
  0.80 mm done clear
  C)
  0.70mm done clear
  D)
  0.50mm done clear
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• question_answer20)
  Suppose refractive index \[\mu \] is given as\[\mu =A+\frac{B}{\lambda _{{}}^{2}}\] where A and B are constants and \[\lambda \] is wavelength, then dimensions of B are same as that of
  A)
  Wavelength        done clear
  B)
  Volume done clear
  C)
  Pressure done clear
  D)
  Area done clear
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• question_answer21)
  To determine the Young's modulus of a wire, the formula is \[Y=\frac{F}{A}\times \frac{L}{\Delta L}\]; where L = length, A = area of cross- section of the wire, \[\Delta L\]= change in length of the wire when stretched with a force \[F\]. What is the conversion factor to change it from CGS to MKS system?
  A)
  0.1 done clear
  B)
  0.2 done clear
  C)
  0.3 done clear
  D)
  0.4 done clear
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• question_answer22)
  The dimensional formula for a physical quantity \[x\] is\[[{{M}^{-1}}{{L}^{3}}{{T}^{-2}}]\]. The errors in measuring the quantities M, L, and F, respectively, are 2%, 3%, and 4%. What is the maximum percentage of error that occurs in measuring the quantity x?
  A)
  20 done clear
  B)
  19 done clear
  C)
  21 done clear
  D)
  22 done clear
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• question_answer23)
  If the acceleration due to gravity is \[10m{{s}^{-2}}\] and the units of length and time are changed in kilometer and hour respectively, what is the numerical value of the acceleration?
  A)
  129800 done clear
  B)
  130000 done clear
  C)
  129600 done clear
  D)
  128000 done clear
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• question_answer24)
  The wavelength associated with a moving particle depends upon \[{{p}^{th}}\]power of its mass m, \[{{q}^{th}}\]power of its velocity v and \[{{r}^{th}}\] power of Planck's constant h. Then the sum of values of \[p\], q and r is -K. Find the value of K7.
  A)
  2 done clear
  B)
  4 done clear
  C)
  5 done clear
  D)
  1 done clear
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• question_answer25)
  The mass of a body is 20.000 g and its volume is 10.00 \[c{{m}^{3}}\]. If the measured values are expressed to the correct significant figures, find the maximum error in the value of density in \[(g\,c{{m}^{-3}})\].
  A)
  0.003 done clear
  B)
  0.001 done clear
  C)
  0.004 done clear
  D)
  0.002 done clear
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