Question

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

• A. $3I$
• B. $7I$
• C. $4I$
• D. $5I$

Answer 1

The correct option is B $7I$

The moment of inertia of a sphere about its diameter is given as,

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

The moment of inertia of the sphere about the tangent is given as,

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

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

The total moment of inertia of both spheres about the common tangent is given as,

$I_t=2I^{\prime }$

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

$I_t=7I$