Q 11-01-104JEE MainJEE Main 2024 (27 Jan, Shift 1)Easy
Given below are two statements:
Statement (I): Planck's constant and angular momentum have the same dimensions.
Statement (II): Linear momentum and moment of force have the same dimensions.
In light of the above statements, choose the correct answer from the options given below:
Answer: (A) Statement I is true but Statement II is false
Planck's constant: $[h] = [E]/[\nu] = \text{J s} = [\text{ML}^2\text{T}^{-1}]$, and angular momentum $L = mvr$ also has $[\text{ML}^2\text{T}^{-1}]$. Statement I is true.
Linear momentum $p = mv$ has $[\text{MLT}^{-1}]$, while moment of force (torque) $\tau = rF$ has $[\text{ML}^2\text{T}^{-2}]$. They differ, so Statement II is false.
Solution by Sreeraj P, M.Sc Physics