Question

A hollow sphere of mass $1kg$ and radius $10cm$ is free to rotate about its diameter. If a force of $30N$ is applied tangentially to it, its angular acceleration is (in\ $rad/s^2$)

• A. $5000$
• B. $450$
• C. $50$
• D. $5$

Answer 1

The correct option is B $450$

Given mass $m=1kg$ , Radius $R=10cm=0.1m$, $F=30N$

Moment of inertia about centre $I=\frac{2}{3}m{R}^2=\frac{2}{3}\times 1\times {0.1}^2=\frac{2}{300}$.

Let angular acceleration is $\alpha$.

$\therefore$ Taking moment about centre of hollow sphere. $\Rightarrow T=I\alpha$

$\Rightarrow F\times R=I\alpha$ $\Rightarrow 30\times 0.1=\frac{2}{300}\times \alpha$ $\Rightarrow \alpha =450$ $rad/s^2$