Question

A solid sphere and a hollow sphere each of mass M and radius R are released at the same time from the top of an inclined plane. Which one of the following statements is necessarily true?
A.Both spheres will reach the bottom at the same time.
B. The hollow sphere will reach the bottom with the greater kinetic energy.
C.The solid sphere will reach the bottom first.
D. The hollow sphere will reach the bottom first.
E. The solid sphere will reach the bottom with the greater kinetic energy.

Answer 1

Answer:

C. The solid sphere will reach the bottom first.

E. The solid sphere will reach the bottom with the greater kinetic energy.

Explanation:

To answer this,the sphere that has the smaller mass moment of inertia will be the one that will have the largest acceleration down the plane. And we know that higher acceleration means higher speed.

Now, moment of inertia of both spheres are;

I_solid sphere = (2/5)mr² = 0.4mr²

I_hollow sphere = (2/3)mr² = 0.67 mr²

Now, it is clear that the solid sphere has the smaller mass moment of inertia. This means that the solid sphere will have more acceleration and as well higher speed and will thus reach the bottom first.

Also, the higher the speed, the higher the kinetic energy since K.E = ½mv².

Thus, options C & E are correct.