HELP - ROTATIONAL INERTIA (no numbers given)

[Quarkn]

Homework Statement

A bowling ball made for a child has half the radius of an adult bowling ball. They are made of the same material (and therefore have the same mass per unit volume). By what factor is a) mass and b) rotational inertia if the child's ball reduced compared with the adult ball?

Homework Equations

I=MR²
(sphere) I=(2/5)MR²

The Attempt at a Solution

I only got to: R(adult) = (1/2)R (child).

PS. the answers to a) reduced by a factor of 8 and b)reduced by a factor of 32

 

[physicsvalk]

Set the two densities equal to each other, and then examine how the masses vary (since the radius of the child's bowling ball differs from the adult's). Based on this, you should have enough information to determine its moment of inertia.

 

[Quarkn]

Set the two densities equal to each other, and then examine how the masses vary (since the radius of the child's bowling ball differs from the adult's). Based on this, you should have enough information to determine its moment of inertia.

So would you find the volume of each spheres first?

And if i set the two densities equal, wouldn't the masses just cancel?

ex. D=M/V, M/v=M/V ?

 

[physicsvalk]

Yes, you would need to find the volumes.

The densities are said to be equal and the volumes differ, therefore, the masses can't be the same.