Question

I hand you two spheres. They have the same mass, the same radius, and the same exterior surface. I claim one is a solid sphere and the other is hollow. Can you determine which is which without cutting them open?

Answer 1

Step-by-step explanation:

Between two spheres of equal masses having equal radius , the one which is hollow will have less moment of inertia and therefore less radius of gyration ( k )

When they are allowed to roll over an inclined plane , they will have acceleration as follows

a = gsinθ / ( 1 + k²/r²)

For hollow sphere , k is less . therefore denominator is less and acceleration is more.

in other words , hollow sphere will have greater acceleration . So it will reach the bottom of an inclined surface in lesser time if allowed to roll over it .

This is how we can identify a hollow sphere without breaking it open .