Question

A solid sphere is rotating about a diameter at an angular velocity $\omega .$ If it coots so that its radius reduces to $\frac{1}{n}$ of its original value, its angular velocity becomes

• A. $\frac{\omega }{n}$
• B. $\frac{\omega }{{{n}^{2}}}$
• C. $n\omega$
• D. ${{n}^{2}}\omega$

Answer 1

Answer: (D)

${{n}^{2}}\omega$

Answer 2

From law of conservation of angular momentum, if no external torque is acting upon a body rotating about an axis, then the angular momentum of the body remains constant that is $J=I \omega$ Also, $I=\frac{2}{5} M R^{2}$ for a solid sphere. Given, $R_{1}=R, R_{2}=\frac{R}{n}$ $\therefore \frac{2}{5} M R^{2} \omega_{1}=\frac{2}{5} M\left(\frac{R}{n}\right)^{2} \times \omega_{2}$ $\Rightarrow \omega_{2}=n^{2} \omega_{1}$ $=m^{2} \omega$