Ihand 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?

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 .

gans

explanation:

vestigial organs (like your appendix) are organs that no longer serve a purpose.

a and b sometimes have a positive value