Mass of a ball with different density

[asi123]

Homework Statement

Hey guys.
Look at this one, I have a ball with density p1 and radius R. Inside the ball they dig another ball with radius R/2 and fill it up with material that has density p2. My question is, why does the mass "m" equals to what they wrote in the answer (marked with red)? why do I need to subtract the densitys in order to find the new mass?
10x.

Homework Equations

The Attempt at a Solution

 

[Doc Al]

M is the mass of a solid ball of density p1 and radius R. But you've cut out a ball of radius R/2 and replaced it with a different density. To find the new mass of the ball: subtract the mass you cut out (p1) and add back the mass you replaced it with (p2).

 

[asi123]

Still, this is what I got (in the pic).

 

[Doc Al]

Looks good to me.

 

[asi123]

Ok, so do you know maybe what is that expression I marked in red could be?

 

[Doc Al]

Ok, so do you know maybe what is that expression I marked in red could be?

Beats me. Where did you get it?

I assume that you've presented the problem accurately: Find the new mass of the large ball?

 

[asi123]

Oh, sorry, I forgot to post the entire problem...
Anyway, they did what they did with ball, then, they put it on a surface with friction, diverted it a bit and then release (by a "bit" I mean that the angle is really small). the question is to find the period time T of the movement of the ball.