Question

Which of the following pairs have same dimensions?
(1) Angular momentum and work
(2) Torque and work
(3) Energy and Young's modulus
(4) Light-year and wavelength

• A. 1, 2 and 3 are correct
• B. 1 and 2 are correct
• C. 2 and 4 are correct
• D. 1 and 3 are correct

Answer 1

Answer: (C)

Torque $=$ Force $\times$ distance
$[\tau ]=\left[M{L}^2{T}^{-2}\right]$
[ Energy] $=$ [work] $=$ Force $\times$ distance
$[E]=[W]=\left[M{L}^2{T}^{-2}\right]$
Angular Momentum $=$ Moment of inertia $\times$ Angular velocity
$[L]=\left[M{L}^2\right]\left[T^{-1}\right]$
$[L]=\left[M{L}^2{T}^{-1}\right]$
Light-year and wavelength have dimensions of length.