QJEEM24Ph8e4b: JEE Main 2024 Physics - Class 11 JEEM24Ph8e4b Solution: The dimensional formula of angular impulse is :

Angular impulse is given when a torque is applied for a certain amount of time. The angular impulse changes the angular momentum of an object and has the same dimensions as angular momentum.

The dimensional formula for torque $\tau$ is the same as that for work, since torque is a kind of rotational work, which is given by force times distance (or in rotational terms, it can be considered as force times lever arm). The dimensional formula for force is $\left[\mathrm{M} \mathrm{L} \mathrm{T}^{-2}\right]$ , and when multiplied by distance $\left[\mathrm{L}\right]$ , we get:

$\left[\mathrm{Torque}\right] = \left[\mathrm{M} \mathrm{L} \mathrm{T}^{-2}\right] \times \left[\mathrm{L}\right] = \left[\mathrm{M} \mathrm{L}^2 \mathrm{T}^{-2}\right]$

Now, angular impulse is torque times time, so we multiply the dimension of torque by time $\left[\mathrm{T}\right]$ :

$\left[\mathrm{Angular\ Impulse}\right] = \left[\mathrm {M} \mathrm{L}^2 \mathrm{T}^{-2}\right] \times \left[\mathrm{T}\right] = \left[\mathrm{M} \mathrm{L}^2 \mathrm{T}^{-1}\right]$

So the correct dimensional formula for angular impulse is given by Option C, which is $\left[\mathrm{M} \mathrm{L}^2 \mathrm{T}^{-1}\right]$ .