Question

The radius of gyration of a hollow spherical shell is $2.5J$. 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 $:K_{\text{rot }}=2.5J,{\omega }_1=\omega ,{\omega }_2=10\omega$
Rotational kinetic energy
$K_{\text{rot }}=\frac{1}{2}I{\omega }^2$
or $K_{\text{rot }}\propto {\omega }^2$
$\therefore \frac{K_{\text{rot }}^{\prime }}{K_{\text{rot }}^{\prime }}={\left(\frac{{\omega }_2}{{\omega }_1}\right)}^2=(10{)}^2=100$
$\therefore K_{\text{rot }}^{\prime }=100\times 2.5=250J$