IIT-JEE 2012 · Paper 1 · Physics Q1

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PhysicsSingle correct+3 / -1Question 1 of 60

A thin uniform rod, pivoted at $O$ , is rotating in the horizontal plane with constant angular speed $\omega$ , as shown in the figure. At time $t=0$ , a small insect starts from $O$ and moves with constant speed $v$ with respect to the rod towards the other end. It reaches the end of the rod at $t=T$ and stops. The angular speed of the system remains $\omega$ throughout. The magnitude of the torque $(|\vec\tau|)$ on the system about $O$ , as a function of time is best represented by which plot?

A horizontal rod pivoted at O on a vertical z-axis, rotating with angular speed ω; an insect on the rod moves outward with speed v.

|τ| against t: rises linearly from 0 until t = T, then stays constant.

|τ| against t: rises linearly from 0 until t = T, then drops to zero (dashed vertical line at T).

|τ| against t: rises as a concave-up curve until t = T, then stays constant.

|τ| against t: rises as a concave-up curve until t = T, then drops to zero.

Answer and worked solution

Official answer: B

Angular momentum about O. The rod's own angular momentum is constant. The insect is at $r=vt$ , so its angular momentum is $m r^2\omega=m v^2\omega t^2$ .

Torque.
$|\vec\tau|=\frac{dL}{dt}=2mv^2\omega t\quad(0<t<T),$
which grows linearly. After $t=T$ the insect stops at the end, $L$ is constant and the torque is zero.

(B)

Topics:Angular momentum and its conservation Torque and rotational dynamics

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IIT-JEE 2012 · Paper 1, Physics question 1