BITSAT 2024 Shift 1 Paper

The angular velocity of the rigid body is given by ω=α−βt, where α and β are constants. By comparing this with the equation ω=ω0−αt, we can identify the initial angular velocity ω0 as α and the angular retardation (or deceleration) as β.
To find the angle through which the body rotates before it comes to a stop, we use the kinematic equation for rotational motion:
ω2=ω02+2βθ
We know that when the body stops, ω=0. Therefore, by substituting into the equation, we get:
0=α2−2βθ
Solving for θ, the angle rotated, we find:
θ=‌

α2

2β

Thus, the angle through which the body rotates before stopping is ‌

α2

2β

.