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 i

Question

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 x 7 . The value of x is ______.

TestHub · Accepted Answer

Moment of inertia of the solid sphere about any diameter is given by, $\frac{2 m_{1} R^{2}}{5}$ .

Using parallel axis theorem, we get

$I_{solid sphere} = \frac{2}{5} m_{1} R^{2} + m_{1} R^{2} = \frac{7}{5} m_{1} R^{2}$

$= \frac{7}{5} \times 5 R^{2}$

$= 7 R^{2}$

Moment of inertia of the disc about the diameter is given by, $\frac{m_{2} R^{2}}{4}$ .

Now using parallel axis theorem, we get

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

$= \frac{5}{4} \times 4 R^{2}$

$= 5 R^{2}$

Therefore, $\frac{I_{disc}}{I_{soild sphere}} = \frac{5}{7}$

Thus, $x = 5$ .

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