Question

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 $|\tau|$ on the system about O, as a function of time is best represented by which plot?

• A.
• B.
• C.
• D.

Answer 1

Answer: (B)

Answer 2

$|L|$ or $L=I\omega$ (about axis of rod)
$I=I_{rod}+mx^2=I_{rod}+mv^2t^2$
Here m = mass of insect
$\therefore L=(I_{rod}+mv^2t^2)\omega$
Now $|\tau|=\frac{dL}{dt}=(2mv^2t\omega)$ or $|\tau|?t$
i.e. the graph is straight line passing through origin.
After time T,L = constant
$\therefore |\tau|$ or $\frac{dL}{dt}=0$