JEE Main 2022 · 27 Jul · Shift 1 · Physics Q59

← JEE Main 2022 · 27 Jul · Shift 1

PhysicsInteger+4 / -1Question 59 of 90

A pulley of radius 1.5 m is rotated about its axis by a force $F=\left(12t-3t^2\right)$ N applied tangentially (while t is measured in seconds). If moment of inertia of the pulley about its axis of rotation is 4.5 kg m $^2$ , the number of rotations made by the pulley before its direction of motion is reversed, will be $\dfrac K\pi$ . The value of K is ______.

Your answer

Answer and worked solution

Official answer: 18

Angular acceleration $\alpha=\frac{1.5(12t-3t^2)}{4.5}=4t-t^2$ , so $\omega=2t^2-\frac{t^3}3$ , zero again at $t=6$ s.

Angle $\theta=\int_0^6\omega\,dt=144-108=36$ rad, i.e. $\frac{18}\pi$ rotations.

Answer: 18

Topics:Torque and rotational dynamics

← Previous question Next question →

JEE Main 2022 · 27 Jul · Shift 1, Physics question 59