Question

If a solid sphere of mass $5kg$ and a disc of mass $4$ have the same radius. Then the ratio of moment of inertia of the disc about a tangent in its plane to the moment of inertia of the sphere about its tangent will be $\frac{x}{7}$. The the value of $x$ is ___

Answer 1

Answer: 5

$I_1=\frac{2}{5}{m}_1{R}^2+m_1{R}^2$
$I_1=m_1{R}^2\left(\frac{7}{5}\right)$
$I_1=7R^2$

$I_2=\frac{m_2{R}^2}{4}+m_2{R}^2$
$I_2=\frac{5}{4}{m}_2{R}^2$
$I_2=5R^2$
$\frac{I_2}{I_1}=\frac{5}{7}$
$x=5$