A solid sphere and a disc of same mass ' $M$ 'and radius ' $R$ ' are kept such that their curved surfaces are in contact and their centers lie along the same horizontal line. The moment of inertia of the two body system about an axis passing through their point of contact and perpendicular to the plane of the disc is

• A

  $\frac{53 M R^2}{20}$
• B

  $\frac{39 M R^2}{10}$
• Correct answer
  C

  $\frac{29 M R^2}{10}$
• D

  $\frac{9 M R^2}{10}$

Solution

$\mathrm{I}_1=\frac{2}{5} \mathrm{MR}^2+\mathrm{MR}^2=\frac{7}{5} \mathrm{MR}^2$
$\mathrm{I}_2=\frac{1}{2} \mathrm{MR}^2+\mathrm{MR}^2=\frac{3}{2} \mathrm{MR}^2$ $\therefore$ Moment of inertia about point of contact, $\mathrm{I}=\mathrm{I}_1+\mathrm{I}_2=\left(\frac{7}{5}+\frac{3}{2}\right) \mathrm{MR}^2=\frac{29 \mathrm{MR}^2}{10}$

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