If the spherical planet of mass ' $\mathrm{M}^{\prime}$ and radius 'R' suddenly shrinks to half its size,…

If the spherical planet of mass ' $\mathrm{M}^{\prime}$ and radius 'R' suddenly shrinks to half its size, its mass reduces to half. The new moment of inertia of the planet about its diameter is
  1. $\frac{\mathrm{MR}^{2}}{10}$
  2. $\frac{\mathrm{MR}^{2}}{20}$
  3. $\frac{2}{3} \mathrm{MR}^{2}$
  4. $\frac{2}{5} \mathrm{MR}^{2}$

Solution

$\mathrm{I}_{1}=\frac{2}{5} \mathrm{MR}^{2}$ $\mathrm{I}_{2}=\frac{2}{5} \frac{M}{2} \times\left(\frac{R}{2}\right)^{2}=\frac{2}{5} \times \frac{M}{2} \times \frac{R^{2}}{4}=\frac{M R^{2}}{20}$

Asked in: MHT CET 2020 (20 Oct Shift 2)

Practice more Rotational Motion questions on Aicharya