Q131 / 160 · AP EAMCET 2021 (20 Aug Shift 2) · Physics

As solid sphere of mass ' $M$ ' and radius ' $R$ ' spins about an axis passing through its centre making $600 rpm$ . Its kinetic energy of rotation is

Solution

Rotational kinetic energy, $K . E = \frac{1}{2} I ω^{2}$

$\Rightarrow K . E = \frac{1}{2} \times \frac{2}{5} M R^{2} \times {(\frac{600 \times 2 π}{60})}^{2}$

$\Rightarrow K . E = \frac{1}{5} M R^{2} \times {(20 π)}^{2}$

$\Rightarrow K . E = \frac{1}{5} M R^{2} \times 400 π^{2}$

$\Rightarrow K . E = 80 π^{2} M R^{2}$

Hence, the correct answer is option: 'D'.