Question

The radius of gyration of a hollow spherical shell is $2.5\, J$. If its frequency of rotation is made 10 times, then new kinetic energy will be:

• A. 250 J
• B. 0.25 J
• C. 2500 J
• D. 2.5 J

Answer 1

Answer: (A)

Given $: K_{ \text{rot }}=2.5\, J , \omega_{1}=\omega, \omega_{2}=10 \omega$
Rotational kinetic energy
$K_{\text {rot }}=\frac{1}{2} I \omega^{2}$
or $K_{\text{rot }} \propto \omega^{2}$
$\therefore \frac{K_{\text {rot }}'}{K_{\text {rot }}'}=\left(\frac{\omega_{2}}{\omega_{1}}\right)^{2}=(10)^{2}=100 $
$ \therefore K_{\text {rot }}'=100 \times 2.5=250\, J $