. Three bodies a ring a solid cylinder and a solid sphere roll
down the same inclined plane without slipping. They start from rest. The radii of the bodies are identical.
Which of the bodies reaches the ground with maximum velocity?
The conservation of energy says that
mgh=1 /2mv2(1+ k2 /R2) [All the alphabet carries it own significance]
v2=2gh /1+k2 /R2
For the ring R=k
For the cylinder k2=R2 /2
So the velocity will be
v2=2gh /1+1 /2
v= √4gh /3
For a solid sphere k2=2 /5R2
v=√2gh /1+2 /5
Among the given three bodies the solid sphere has the greatest and the ring has the least velocity at the bottom of the inclined plane.