Question

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 hte rod at \(t=T\) and stops. The angulr speed of the system remains \(\omega\) throughout. The magnitude of the torque \((|\overrightarrow{\tau}|)\) on the system about \(O\), as a function of time is best represented by which plot?


(i)

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

$\tau =\frac{d}{dt}\left(l\omega \right)$
$=\frac{d}{dt}(\frac{M{L}^2}{3}+m{x}^2)\omega$
$=2mx\frac{dx}{dt}\omega$
Now, $x=vt$
$\Rightarrow \tau \propto t$
Finally torque becomes zero.