Question

A circular disc of radius $10cm$ is free to rotate about an axis passing through its centre without friction and its moment of inertia is $\frac{1}{2}\pi kg{m}^2$. A tangential force of $20N$ is acting on the disc along its rim. Starting from rest, the number of rotations made by the disc in $10s$ is:

• A. $50$
• B. $100$
• C. $150$
• D. $200$

Answer 1

The correct option is B $100$

Torque on the disc $\tau =F\times R=20\times 0.1=2Nm$
Given moment of inertia $I=\frac{1}{2\pi }kg{m}^2$
$\tau =I\alpha$
$\Rightarrow \alpha =4\pi rad{s}^{-2}$
No. of rotations made $=\frac{\left(\frac{1}{2}\alpha t^2\right)}{2\pi }$ (by the 1st law of uniform angular rotation)
$=\frac{\frac{1}{2}\times 4\pi \times 100}{2\pi }$
$=100$