Published by:
CGP EDU Academic Team
Published on: September 12, 2026
Which of the following pairs of physical quantities has the same dimensions
Text Solution
Verified by ExpertsThe correct answer is:
D
Step 1: Identify the dimensions of each quantity involved in the options.
Work (W) is defined as the product of force (F) and displacement (s).
W = F × s.
The dimensions of force are given by:
F = mass × acceleration = M L T^{-2}, where M is mass, L is length, and T is time.
Thus, the dimensions of work are:
[Work] = [Force] × [Displacement] = M L T^{-2} × L = M L^2 T^{-2}.
Step 2: Now examine the dimensions of energy. Energy (E) is also defined as work done (Joule) and has the same dimensional formula.
Therefore, [Energy] = M L^2 T^{-2}.
Step 3: Compare the dimensions from options A, B, and C with work and energy:
- Option A: Work (M L^2 T^{-2}) and Power (P = Work/T) = M L^2 T^{-3}. Different dimensions.
- Option B: Momentum (p = M L T^{-1}) which is different from Energy (M L^2 T^{-2}).
- Option C: Force (M L T^{-2}) and Power (M L^2 T^{-3}). Different dimensions.
Conclusion: The only pair with the same dimensions is Work and Energy.
Therefore, the correct answer is Option D.
Work (W) is defined as the product of force (F) and displacement (s).
W = F × s.
The dimensions of force are given by:
F = mass × acceleration = M L T^{-2}, where M is mass, L is length, and T is time.
Thus, the dimensions of work are:
[Work] = [Force] × [Displacement] = M L T^{-2} × L = M L^2 T^{-2}.
Step 2: Now examine the dimensions of energy. Energy (E) is also defined as work done (Joule) and has the same dimensional formula.
Therefore, [Energy] = M L^2 T^{-2}.
Step 3: Compare the dimensions from options A, B, and C with work and energy:
- Option A: Work (M L^2 T^{-2}) and Power (P = Work/T) = M L^2 T^{-3}. Different dimensions.
- Option B: Momentum (p = M L T^{-1}) which is different from Energy (M L^2 T^{-2}).
- Option C: Force (M L T^{-2}) and Power (M L^2 T^{-3}). Different dimensions.
Conclusion: The only pair with the same dimensions is Work and Energy.
Therefore, the correct answer is Option D.
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