Question

Two spheres of mass and radius same are in contact with each other. If the moment of inertia of a sphere about its diameter is $I$ the moment of inertia of both the spheres about the tangent at their common point would be?

Answer 1

Two sphere of mass and radius same are in contact with each other. If the moment of inertia of a sphere, about its diameter, is $I$. The moment of inertia of both the sphere about the tangent at their common point would be:-

$I=\frac{2}{5}M{R}^2{I}^{\prime }=2\frac{2}{5}M{R}^2+M{R}^2=\frac{14}{5}M{R}^2$

Where moment of inertia of a sphere about its diameter,

$I=\frac{2}{5}M{R}^2$

Moment of inertia of the sphere about the tangential:-

From parallel axis theorem:-

$I^{\prime }=\frac{2}{5}M{R}^2+M{R}^2=\frac{7}{5}M{R}^2$

Since in the problem about we have two spheres, the moment of inertia $=2\left(\frac{7}{5}M{R}^2\right)=\frac{14}{5}M{R}^2$

We can write the fraction.