Physics MCQs
1. Which of the following represents the dimensions of Farad
(a) \(M^{-1}L^{-2}T^4I^2\)
(b) \(ML^2T^{-2}I^{-2}\)
(c) \(M^{-1}L^{-2}T^2I^2\)
(d) \(ML^2T^{-2}\)
Correct Answer: (a) \(M^{-1}L^{-2}T^4I^2\)
The Farad is the unit of capacitance. Capacitance is given by \(C = Q/V\). The dimensional formula is derived from \([C] = [Q]/[V] = IT/(ML^2T^{-3}I^{-1}) = M^{-1}L^{-2}T^4I^2\).
2. If \(L\), \(C\) and \(R\) denote the inductance, capacitance and resistance respectively, the dimensional formula for \(LC\) is
(a) \([M^0L^0T^2]\)
(b) \([ML^2T^{-1}I^{-2}]\)
(c) \([M^{-1}L^{-2}T^4I^2]\)
(d) \([M^0L^0T^{-2}]\)
Correct Answer: (a) \([M^0L^0T^2]\)
The product \(LC\) has dimensions of time squared. \([L] = [ML^2T^{-2}I^{-2}]\) and \([C] = [M^{-1}L^{-2}T^4I^2]\), so \([LC] = [M^0L^0T^2]\).
3. Dimensional formula \(ML^{-1}T^{-2}\) does not represent the physical quantity
(a) Young's modulus of elasticity
(b) Stress
(c) Strain
(d) Pressure
Correct Answer: (c) Strain
Strain is a dimensionless quantity (ratio of lengths), while the others have dimensions of \(ML^{-1}T^{-2}\).
4. Dimensional formula \(ML^2T^{-3}\) represents
(a) Force
(b) Power
(c) Energy
(d) Work
Correct Answer: (b) Power
Power is energy per unit time, so its dimensions are \(ML^2T^{-3}\).
5. Whose dimensions is \(ML^2T^{-1}\)
(a) Torque
(b) Angular momentum
(c) Power
(d) Work
Correct Answer: (b) Angular momentum
Angular momentum \(L = mvr\) has dimensions \(ML^2T^{-1}\).
6. If \(L\) and \(R\) are respectively the inductance and resistance, then the dimensions of \(L/R\) will be
(a) \(T\)
(b) \(T^{-1}\)
(c) \(T^2\)
(d) Cannot be represented in terms of \(M\), \(L\), \(T\)
Correct Answer: (a) \(T\)
\([L] = ML^2T^{-2}I^{-2}\), \([R] = ML^2T^{-3}I^{-2}\), so \([L/R] = T\).
7. Which pair has the same dimensions
(a) Work and power
(b) Density and relative density
(c) Momentum and impulse
(d) Stress and strain
Correct Answer: (c) Momentum and impulse
Both momentum (\(p = mv\)) and impulse (\(J = FΔt\)) have dimensions \(MLT^{-1}\).
8. Dimensional formula for latent heat is
(a) \(ML^2T^{-2}\)
(b) \(L^2T^{-2}\)
(c) \(MLT^{-2}\)
(d) \(M^0L^2T^{-2}\)
Correct Answer: (d) \(M^0L^2T^{-2}\)
Latent heat is energy per unit mass, so its dimensions are \(L^2T^{-2}\).
9. Dimensional formula for volume elasticity is
(a) \(ML^{-1}T^{-2}\)
(b) \(ML^{-2}T^{-2}\)
(c) \(MLT^{-2}\)
(d) \(M^0L^0T^0\)
Correct Answer: (a) \(ML^{-1}T^{-2}\)
Volume elasticity (bulk modulus) has same dimensions as pressure: \(ML^{-1}T^{-2}\).
10. The dimensions of universal gravitational constant are
(a) \(M^{-1}L^3T^{-2}\)
(b) \(ML^2T^{-2}\)
(c) \(ML^{-1}T^{-2}\)
(d) \(M^0L^2T^{-2}\)
Correct Answer: (a) \(M^{-1}L^3T^{-2}\)
From Newton's law of gravitation \(F = G\frac{m_1m_2}{r^2}\), we get \([G] = M^{-1}L^3T^{-2}\).
11. The dimensional formula of angular velocity is
(a) \(M^0L^0T^{-1}\)
(b) \(MLT^{-1}\)
(c) \(M^0L^0T^1\)
(d) \(ML^0T^{-2}\)
Correct Answer: (a) \(M^0L^0T^{-1}\)
Angular velocity is angle per unit time, so its dimensions are \(T^{-1}\).
12. The dimensions of power are
(a) \(ML^2T^{-3}\)
(b) \(MLT^{-2}\)
(c) \(ML^2T^{-2}\)
(d) \(M^0L^2T^{-2}\)
Correct Answer: (a) \(ML^2T^{-3}\)
Power is energy per unit time, so its dimensions are \(ML^2T^{-3}\).
13. The dimensions of couple are
(a) \(ML^2T^{-2}\)
(b) \(MLT^{-2}\)
(c) \(ML^{-1}T^{-2}\)
(d) \(M^0L^2T^{-2}\)
Correct Answer: (a) \(ML^2T^{-2}\)
Couple is force × distance, same dimensions as work/energy: \(ML^2T^{-2}\).
14. Dimensional formula for angular momentum is
(a) \(ML^2T^{-2}\)
(b) \(MLT^{-1}\)
(c) \(ML^2T^{-1}\)
(d) \(ML^{-1}T^{-1}\)
Correct Answer: (c) \(ML^2T^{-1}\)
Angular momentum \(L = mvr\) has dimensions \(ML^2T^{-1}\).
15. The dimensional formula for impulse is
(a) \(MLT^{-2}\)
(b) \(ML^2T^{-1}\)
(c) \(MLT^{-1}\)
(d) \(M^0L^0T^{-1}\)
Correct Answer: (c) \(MLT^{-1}\)
Impulse is force × time, so dimensions are \(MLT^{-1}\) (same as momentum).
16. The dimensional formula for the modulus of rigidity is
(a) \(ML^2T^{-2}\)
(b) \(MLT^{-2}\)
(c) \(ML^{-1}T^{-2}\)
(d) \(ML^{-1}T^{-1}\)
Correct Answer: (c) \(ML^{-1}T^{-2}\)
Modulus of rigidity has same dimensions as pressure/stress: \(ML^{-1}T^{-2}\).
17. The dimensional formula for Planck's constant \(h\)
(a) \(ML^2T^{-1}\)
(b) \(MLT^{-2}\)
(c) \(ML^2T^{-2}\)
(d) \(ML^{-1}T^{-1}\)
Correct Answer: (a) \(ML^2T^{-1}\)
From \(E = hν\), \([h] = [E]/[ν] = ML^2T^{-2}/T^{-1} = ML^2T^{-1}\).
18. Out of the following, the only pair that does not have identical dimensions is
(a) Angular momentum and Planck's constant
(b) Moment of inertia and moment of a force
(c) Work and torque
(d) Impulse and momentum
Correct Answer: (b) Moment of inertia and moment of a force
Moment of inertia (\(ML^2\)) and moment of force (\(ML^2T^{-2}\)) have different dimensions.
19. The dimensional formula for impulse is same as the dimensional formula for
(a) Momentum
(b) Force
(c) Rate of change of momentum
(d) Torque
Correct Answer: (a) Momentum
Both impulse and momentum have dimensions \(MLT^{-1}\).
20. In the following list, the only pair which have different dimensions, is
(a) Linear momentum and moment of a force
(b) Planck's constant and angular momentum
(c) Pressure and modulus of elasticity
(d) Torque and potential energy
Correct Answer: (a) Linear momentum and moment of a force
Linear momentum (\(MLT^{-1}\)) and moment of force (\(ML^2T^{-2}\)) have different dimensions.
21. If \(R\) and \(L\) represent respectively resistance and self inductance, which of the following combinations has the dimensions of frequency
(a) \(R/L\)
(b) \(L/R\)
(c) \(\sqrt{R/L}\)
(d) \(\sqrt{L/R}\)
Correct Answer: (a) \(R/L\)
\([R] = ML^2T^{-3}I^{-2}\), \([L] = ML^2T^{-2}I^{-2}\), so \([R/L] = T^{-1}\) (frequency).
22. Planck's constant has the dimensions (unit) of
(a) Energy
(b) Linear momentum
(c) Work
(d) Angular momentum
Correct Answer: (d) Angular momentum
Both Planck's constant and angular momentum have dimensions \(ML^2T^{-1}\).
23. The equation of state of some gases can be expressed as \((P + a/V^2)(V - b) = RT\). Here \(P\) is the pressure, \(V\) is the volume, \(T\) is the absolute temperature and \(a\), \(b\) are constants. The dimensions of \(a\) are
(a) \(ML^5T^{-2}\)
(b) \(ML^{-1}T^{-2}\)
(c) \(M^0L^3T^0\)
(d) \(M^0L^6T^0\)
Correct Answer: (a) \(ML^5T^{-2}\)
From the term \(a/V^2\), \([a] = [P][V^2] = ML^{-1}T^{-2} × L^6 = ML^5T^{-2}\).
24. Of the following quantities, which one has dimensions different from the remaining three
(a) Energy per unit volume
(b) Force per unit area
(c) Product of voltage and charge per unit volume
(d) Angular momentum per unit mass
Correct Answer: (d) Angular momentum per unit mass
First three have dimensions \(ML^{-1}T^{-2}\), while (d) has \(L^2T^{-1}\).
25. 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) \(\frac{mr}{\eta}\)
(b) \(\frac{m}{\eta r}\)
(c) \(\frac{m}{\eta r^2}\)
(d) None of the above
Correct Answer: (b) \(\frac{m}{\eta r}\)
\([\eta] = ML^{-1}T^{-1}\), so \([m/(ηr)] = M/(ML^{-1}T^{-1}×L) = T\).
26. 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
(a) \(v \propto \sqrt{g\lambda}\)
(b) \(v \propto \sqrt{\rho g\lambda}\)
(c) \(v \propto \sqrt{g/\lambda}\)
(d) \(v \propto \sqrt{1/g\lambda}\)
Correct Answer: (a) \(v \propto \sqrt{g\lambda}\)
Using dimensional analysis, \(v = k\sqrt{g\lambda}\) satisfies dimensional consistency.
27. The dimensions of Farad are
(a) \(M^{-1}L^{-2}T^4I^2\)
(b) \(ML^2T^{-2}I^{-2}\)
(c) \(M^{-1}L^{-2}T^2I^2\)
(d) \(ML^2T^{-2}\)
Correct Answer: (a) \(M^{-1}L^{-2}T^4I^2\)
Capacitance has dimensions \(M^{-1}L^{-2}T^4I^2\) (same as question 1).
28. The dimensions of resistivity in terms of \(M\), \(L\), \(T\) and \(Q\) where \(Q\) stands for the dimensions of charge, is
(a) \(ML^2T^{-1}Q^{-2}\)
(b) \(ML^3T^{-1}Q^{-2}\)
(c) \(ML^3T^{-2}Q^{-1}\)
(d) \(ML^2T^{-2}Q^{-1}\)
Correct Answer: (b) \(ML^3T^{-1}Q^{-2}\)
Resistivity \(\rho = RA/l\) has dimensions \(ML^3T^{-1}Q^{-2}\).
29. The dimensions of coefficient of thermal conductivity is
(a) \(MLT^{-3}K^{-1}\)
(b) \(ML^2T^{-2}K^{-1}\)
(c) \(MLT^{-2}K^{-1}\)
(d) \(ML^2T^{-3}K^{-1}\)
Correct Answer: (a) \(MLT^{-3}K^{-1}\)
From Fourier's law, \([k] = [Q]/([A][t][ΔT/L]) = MLT^{-3}K^{-1}\).
30. Dimensional formula of capacitance is
(a) \(M^{-1}L^{-2}T^4I^2\)
(b) \(ML^2T^{-2}I^{-2}\)
(c) \(M^{-1}L^{-2}T^2I^2\)
(d) \(ML^2T^{-2}\)
Correct Answer: (a) \(M^{-1}L^{-2}T^4I^2\)
Same as question 1 and 27 - standard dimensions of capacitance.
31. \(ML^2T^{-3}\) represents the dimensional formula of
(a) Power
(b) Momentum
(c) Force
(d) Couple
Correct Answer: (a) Power
Power has dimensions \(ML^2T^{-3}\) (energy per unit time).
32. Dimensional formula of heat energy is
(a) \(ML^2T^{-2}\)
(b) \(ML^2T^{-3}\)
(c) \(MLT^{-2}\)
(d) None of these
Correct Answer: (a) \(ML^2T^{-2}\)
Heat energy has same dimensions as work: \(ML^2T^{-2}\).
33. If \(C\) and \(L\) denote capacitance and inductance respectively, then the dimensions of \(1/\sqrt{LC}\) are
(a) \(M^0L^0T^{-1}\)
(b) \(M^0L^0T^1\)
(c) \(M^0L^0T^0\)
(d) \(M^1L^0T^{-1}\)
Correct Answer: (a) \(M^0L^0T^{-1}\)
\(1/\sqrt{LC}\) has dimensions of frequency (\(T^{-1}\)).
34. Which of the following quantities has the same dimensions as that of energy
(a) Power
(b) Force
(c) Momentum
(d) Work
Correct Answer: (d) Work
Both work and energy have dimensions \(ML^2T^{-2}\).
35. The dimensions of "time constant" \(L/R\) during growth and decay of current in all inductive circuit is same as that of
(a) Constant
(b) Resistance
(c) Current
(d) Time
Correct Answer: (d) Time
\(L/R\) has dimensions of time (\(T\)).
36. Which of the following pairs of physical quantities has the same dimensions
(a) Work and power
(b) Momentum and energy
(c) Force and power
(d) Work and energy
Correct Answer: (d) Work and energy
Both work and energy have dimensions \(ML^2T^{-2}\).
37. The velocity of a freely falling body changes as \(g^ph^q\) where \(g\) is acceleration due to gravity and \(h\) is the height. The values of \(p\) and \(q\) are
(a) \(p = 1, q = 1/2\)
(b) \(p = 1/2, q = 1/2\)
(c) \(p = 1/2, q = 1\)
(d) \(p = 1, q = 1\)
Correct Answer: (b) \(p = 1/2, q = 1/2\)
From \(v = \sqrt{2gh}\), we get \(p = 1/2\) and \(q = 1/2\).
38. Which one of the following does not have the same dimensions
(a) Work and energy
(b) Angle and strain
(c) Relative density and refractive index
(d) Planck constant and energy
Correct Answer: (d) Planck constant and energy
Planck constant (\(ML^2T^{-1}\)) and energy (\(ML^2T^{-2}\)) have different dimensions.
39. The quantity \(\frac{\epsilon_0LV}{t}\): \(\epsilon_0\) 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
(a) Resistance
(b) Charge
(c) Voltage
(d) Current
Correct Answer: (d) Current
\([\epsilon_0] = M^{-1}L^{-3}T^4I^2\), \([LV/t] = L^2T^{-1}V\), so overall dimensions are \(I\) (current).
40. The expression \(\frac{1}{2}mv^2\) represents
(a) Pressure
(b) Kinetic energy
(c) Momentum
(d) Power
Correct Answer: (b) Kinetic energy
Standard formula for kinetic energy.
41. The dimensions of physical quantity \(X\) in the equation Force \(= X\) × Density is given by
(a) \(M^0L^4T^{-2}\)
(b) \(M^0L^{-4}T^{-2}\)
(c) \(M^0L^2T^{-2}\)
(d) \(M^0L^{-2}T^{-2}\)
Correct Answer: (a) \(M^0L^4T^{-2}\)
\([X] = [F]/[Density] = MLT^{-2}/(ML^{-3}) = L^4T^{-2}\).
42. The Martians use force \(F\), acceleration \(a\) and time \(T\) as their fundamental physical quantities. The dimensions of length on Martians system are
(a) \(FT^2\)
(b) \(F^{-1}a^2T^{-1}\)
(c) \(Fa^2T\)
(d) \(aT^2\)
Correct Answer: (d) \(aT^2\)
From \(L = \frac{1}{2}aT^2\), dimensions are \(aT^2\).
43. The dimension of \(\sqrt{LC}\) is that of
(a) Velocity
(b) Time
(c) Capacitance
(d) Distance
Correct Answer: (b) Time
\(\sqrt{LC}\) has dimensions of time (\(T\)).
44. Dimensions of permeability are
(a) \(MLT^{-2}I^{-2}\)
(b) \(MLT^{-2}\)
(c) \(ML^2T^{-2}I^{-2}\)
(d) \(ML^{-1}T^{-2}\)
Correct Answer: (a) \(MLT^{-2}I^{-2}\)
From \(B = μH\), \([μ] = MLT^{-2}I^{-2}\).
45. Dimensional formula of magnetic flux is
(a) \(ML^2T^{-2}I^{-1}\)
(b) \(ML^2T^{-1}I^{-1}\)
(c) \(ML^2T^{-2}I^{-2}\)
(d) \(ML^2T^{-1}I^{-2}\)
Correct Answer: (a) \(ML^2T^{-2}I^{-1}\)
Magnetic flux \(\phi = BA\) has dimensions \(ML^2T^{-2}I^{-1}\).
46. 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 \(x\) and \(y\) such that \(P^xc^yQ\) is dimensionless, are
(a) \(x = 1, y = 1\)
(b) \(x = -1, y = 1\)
(c) \(x = 1, y = -1\)
(d) \(x = -1, y = -1\)
Correct Answer: (c) \(x = 1, y = -1\)
Solving dimensionally: \(x = 1, y = -1\) makes the expression dimensionless.
47. Dimensions of kinetic energy are
(a) \(ML^2T^{-2}\)
(b) \(MLT^{-1}\)
(c) \(ML^2T^{-1}\)
(d) \(M^0L^2T^{-2}\)
Correct Answer: (a) \(ML^2T^{-2}\)
Kinetic energy has same dimensions as work: \(ML^2T^{-2}\).
48. Dimensional formula for torque is
(a) \(ML^2T^{-2}\)
(b) \(MLT^{-2}\)
(c) \(ML^{-1}T^{-2}\)
(d) \(M^0L^0T^0\)
Correct Answer: (a) \(ML^2T^{-2}\)
Torque is force × distance, same dimensions as work: \(ML^2T^{-2}\).
49. The pair having the same dimensions is
(a) Angular momentum, work
(b) Work, torque
(c) Potential energy, linear momentum
(d) Kinetic energy, velocity
Correct Answer: (b) Work, torque
Both work and torque have dimensions \(ML^2T^{-2}\).
50. The dimensions of surface tension are
(a) \(ML^{-1}T^{-2}\)
(b) \(MLT^{-2}\)
(c) \(MT^{-2}\)
(d) \(ML^2T^{-2}\)
Correct Answer: (c) \(MT^{-2}\)
Surface tension is force per unit length: \(MT^{-2}\).
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