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 $\frac{x}{7}$. The value of x is ___.

Answer 1

5

Answer 2

The moment of inertia of a disc about a tangent in its plane is $I_{disc} = \frac{5}{4}MR^2$. The moment of inertia of a solid sphere about a tangent axis is $I_{sphere} = \frac{7}{5}MR^2$. Given $M_{disc} = 4$ kg and $M_{sphere} = 5$ kg. $I_{disc} = \frac{5}{4}(4)R^2 = 5R^2$. $I_{sphere} = \frac{7}{5}(5)R^2 = 7R^2$. The ratio is $\frac{I_{disc}}{I_{sphere}} = \frac{5R^2}{7R^2} = \frac{5}{7}$. Given ratio is $\frac{x}{7}$. Therefore, $x=5$.