Question

A solid cylinder, a solid sphere and a hollow sphere each of mass m and radius r are released from the top of a smooth inclined plane. Then which of the bodies has minimum acceleration down the plane?

• A. Solid Cylinder
• B. Solid Sphere
• C. Hollow Sphere
• D. all will have the same value

Answer 1

The correct option is C Hollow Sphere

The object with the smallest mass moment of inertia ($I$) will have the largest acceleration down the plane.

Solid sphere: $I=\frac{2}{5}m{r}^2=0.4$

Solid cylinder: $I=\frac{1}{2}m{r}^2=0.5$

Hollow sphere: $I=\frac{2}{3}m{r}^2=0.7$

Hence the body having minimum acceleration down the plane is hollow sphere.