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