Q.1 Which of the following is not a fundamental quantity?
Length
Mass
Time
Velocity
Explanation - Length, mass, and time are base quantities. Velocity is a derived quantity (length/time).
Correct answer is: Velocity
Q.2 Which physical quantity has the dimension [M L T^-2]?
Force
Work
Pressure
Power
Explanation - Force = Mass × Acceleration = M × L T^-2.
Correct answer is: Force
Q.3 The dimensional formula of Planck’s constant is:
[M L^2 T^-1]
[M L^2 T^-2]
[M L T^-1]
[M L^0 T^-1]
Explanation - Planck’s constant has units of energy × time = (ML^2T^-2)(T) = ML^2T^-1.
Correct answer is: [M L^2 T^-1]
Q.4 The dimensional formula of velocity is:
[M^0 L T^-1]
[M^0 L T^1]
[M L^-1 T^-1]
[M^0 L^2 T^-2]
Explanation - Velocity = Displacement/Time = L/T = [M^0 L T^-1].
Correct answer is: [M^0 L T^-1]
Q.5 Which of the following pairs have the same dimensions?
Work and Torque
Momentum and Power
Energy and Force
Velocity and Acceleration
Explanation - Both work and torque have dimensions ML^2T^-2.
Correct answer is: Work and Torque
Q.6 The SI unit of surface tension is:
N/m
J/m^2
kg/s^2
All of these
Explanation - Surface tension = Force/Length (N/m), also Work/Area (J/m^2), which reduces to kg/s^2.
Correct answer is: All of these
Q.7 If acceleration due to gravity is ‘g’, then time period of a simple pendulum of length L is proportional to:
√L/g
√g/L
L/g
g/L
Explanation - Dimensional analysis gives T ∝ √(L/g).
Correct answer is: √L/g
Q.8 Which of the following is dimensionless?
Reynolds number
Velocity
Energy
Pressure
Explanation - Reynolds number is a ratio of inertial to viscous forces, hence dimensionless.
Correct answer is: Reynolds number
Q.9 What is the dimensional formula of pressure?
[M L^-1 T^-2]
[M L T^-2]
[M L^0 T^-1]
[M L^2 T^-2]
Explanation - Pressure = Force/Area = (MLT^-2)/L^2 = [M L^-1 T^-2].
Correct answer is: [M L^-1 T^-2]
Q.10 The unit of gravitational constant G is:
Nm^2/kg^2
kg m/s^2
m^3/s^2
J/kg
Explanation - From Newton’s law F = Gm1m2/r^2, G = F r^2 / (m1 m2) = Nm^2/kg^2.
Correct answer is: Nm^2/kg^2
Q.11 What is the dimensional formula of energy?
[M L^2 T^-2]
[M L^2 T^-1]
[M L T^-2]
[M L^0 T^-2]
Explanation - Energy = Work = Force × Distance = MLT^-2 × L = ML^2T^-2.
Correct answer is: [M L^2 T^-2]
Q.12 Which one is a non-SI unit of energy?
Joule
Erg
Calorie
Both Erg and Calorie
Explanation - SI unit is Joule, while erg and calorie are non-SI energy units.
Correct answer is: Both Erg and Calorie
Q.13 Dimensional analysis helps to:
Check the correctness of an equation
Find new physical laws
Define fundamental quantities
None of these
Explanation - Dimensional analysis is mainly used to check consistency of equations.
Correct answer is: Check the correctness of an equation
Q.14 If the percentage error in length is 2% and in breadth is 3%, then the error in area is:
1%
5%
6%
None of these
Explanation - Error in product = sum of relative errors = 2% + 3% = 5%.
Correct answer is: 5%
Q.15 If a quantity A = x^2 y, and percentage errors in x and y are 1% and 2% respectively, error in A is:
4%
2%
1%
None of these
Explanation - ΔA/A = 2(Δx/x) + (Δy/y) = 2(1%) + 2% = 4%.
Correct answer is: 4%
Q.16 The least count of a Vernier caliper is:
Difference between 1 main scale division and 1 vernier scale division
Smallest division on main scale
Smallest division on vernier scale
Product of main and vernier scale divisions
Explanation - Least count = 1 MSD − 1 VSD.
Correct answer is: Difference between 1 main scale division and 1 vernier scale division
Q.17 Which of these has the same dimension as impulse?
Momentum
Force
Work
Power
Explanation - Impulse = Force × Time = (MLT^-2)T = MLT^-1, same as momentum.
Correct answer is: Momentum
Q.18 Dimension of universal gas constant R is:
[M L^2 T^-2 K^-1 mol^-1]
[M L^2 T^-1 K^-1 mol^-1]
[M L T^-2]
[M^0 L^2 T^-2]
Explanation - R = PV/nT → (ML^-1T^-2 × L^3)/(mol × K) = ML^2T^-2 K^-1 mol^-1.
Correct answer is: [M L^2 T^-2 K^-1 mol^-1]
Q.19 In which of the following cases is dimensional analysis not useful?
Checking correctness of equation
Finding numerical constants
Deriving relation among quantities
Converting units
Explanation - Dimensional analysis cannot give dimensionless constants.
Correct answer is: Finding numerical constants
Q.20 Which of the following is dimensionally incorrect?
Work = Force × Distance
Power = Work/Time
Pressure = Force/Volume
Velocity = Distance/Time
Explanation - Pressure is Force/Area, not Force/Volume.
Correct answer is: Pressure = Force/Volume
Q.21 Which of the following is a dimensionless quantity?
Strain
Stress
Force constant
Work
Explanation - Strain = Change in length / Original length = dimensionless.
Correct answer is: Strain
Q.22 Dimensional formula of angular momentum is:
[M L^2 T^-1]
[M L^2 T^-2]
[M L T^-1]
[M L^0 T^-1]
Explanation - Angular momentum = mvr = (MLT^-1)L = ML^2T^-1.
Correct answer is: [M L^2 T^-1]
Q.23 If g = 9.8 m/s^2 and error in its measurement is 0.1 m/s^2, percentage error is:
0.1%
0.98%
1.02%
10%
Explanation - Percentage error = (0.1/9.8) × 100 ≈ 1.02%.
Correct answer is: 1.02%
Q.24 Which of the following has unit same as that of torque?
Work
Power
Energy
All of these
Explanation - Both work and torque have same unit Joule = N·m.
Correct answer is: Work
Q.25 Which one is not a unit of time?
Second
Year
Parsec
Day
Explanation - Parsec is a unit of length, not time.
Correct answer is: Parsec