a solid sphere and a hollow sphere have the same mass and radius. they are rotating with the same angular speed. which one has the higher angular momentum?

I. The hollow sphere has the greater angular momentum.

Explanation:

Given that the mass and radius of hollow sphere and solid sphere are same. Let the mass and radius of two spheres be m and r respectively. The two spheres are rotating having same angular velocity ω .

Moment of inertia of solid sphere, I₁ =

Moment of inertia of hollow sphere, I₂ =

Since, I₁ and I₂ are not equal. Therefore, the statement iv is wrong.

The relation between angular momentum, moment of inertia and angular velocity is :

L = Iω

Let L₁ and L₂ be the angular momentum of solid sphere and hollow sphere respectively.

L₁ = I₁ω     and   L₂ = I₂ω

As ω is same for both spheres but I₂ is greater than I₁, hence L₂ is greater than L₁.

Therefore, statement I is correct that the hollow sphere has the greater angular momentum.

Explanation: