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

Options

A. impulse and momentum
B. moment of inertia and moment of force
C. angular momentum and Planck's constant
D. work and torque.

Answer

B

Explanation

Impulse `=Fxxt`
`=(m(v_(2)-v_1))/(t)xxt=m(v_(2)-v_(1))`
=change in momentum
`therefore` [Impulse]=[Momentum]
Planck's constant, [h]=`["energy"]xx ["time"]`
`Rightarrow [Fxxr xx "time"]=(m(v_2-v_1))/(t)xxrxxt`
`Rightarrow m(v_(2)-v_(1))xxr=("change of momentum")xxr` `therefore [h]=[l]`
Work, `W=vecF.vecd."Torque","tau=vecrxxvecF`
`therefore [W]=[tau]`
Moment of inertia `l=mr^(2)="mass " xx ("distance")^(2)`
Moment of force `,tau=vecr xx vec F="distance" xx "force"` `="distance "xx ("change in momentum")/("time")`
`therefore [1] ne [tau]`
Therefore, moment of inertia and moment of force have different dimensions.