Out of the following pair, which one does not have identical dimensions

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CGP EDU Academic Team · Accepted Answer

The correct answer is A. To determine which pair does not have identical dimensions, we need to analyze the dimensions of each option.   Option A: Moment of inertia and moment of force Moment of inertia (I) is given by the formula $I = \sum m r^2$, where $m$ is mass and $r$ is distance. Its dimensions are $[M][L]^2$.  Moment of force (torque, τ) is given by $	au = rF$, where $r$ is distance and $F$ is force. The dimensions of force are $[M][L][T]^{-2}$, so τ has dimensions $[L][M][T]^{-2}$.  These dimensions are not identical.   Option B: Work and torque Work (W) has dimensions $[M][L]^2[T]^{-2}$ and torque’s dimensions are $[M][L]^2[T]^{-2}$. Both are identical.   Option C: Angular momentum and Planck's constant Angular momentum (L) has dimensions $[M][L]^2[T]^{-1}$ and Planck's constant (h) has dimensions $[M][L]^2[T]^{-1}$. Both are identical.   Option D: Impulse and momentum Impulse (J) has dimensions $[M][L][T]^{-1}$ and momentum (p) also has dimensions $[M][L][T]^{-1}$. Both are identical.    Therefore, the pair that does not have identical dimensions is Option A.

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