Question

A hollow sphere and a solid sphere both having same mass of 5 kg and radius 10 meter initially at rest. if they are made to roll down the same inclined plane without slipping, the ratio of their speeds when they reach the ground will be ? please give full solution.

Answer 1

let v1 and v2 be the linear speed of their centre of masses when they reach the ground.
Applying law of conservation ,
mv²+Iw²=2mgh.

=>as it is pore rolling,v=rw
mv²+Iv²/r²=2mgh
=>v²(m+I/r²)=2mgh
=>v=[2mgh/(m+I/r²)]½
Now for the hollow sphere I=2/3mr² and for the solid sphere I=2/5mr².
we can the easily calculate the ratio.