If a solid sphere of mass 5 kg and a disc of mass 4 kg 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 The value of x is __________ .

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Solution

Q.
If a solid sphere of mass 5 kg and a disc of mass 4 kg 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 value of x is __________ . [2023]

Ans.
(5)

$I_{1} = \frac{2}{5} m_{1} R^{2} + m_{1} R^{2} = m_{1} R^{2} (\frac{7}{5})$

$\Rightarrow I_{1} = 7 R^{2}$

$I_{2} = \frac{m_{2} R^{2}}{4} + m_{2} R^{2} = \frac{5}{4} m_{2} R^{2}$

$\Rightarrow I_{2} = 5 R^{2}$

$\frac{I_{2}}{I_{1}} = \frac{5}{7} \Rightarrow x = 5$

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