. 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?

 

Best Answer

Explanation:

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

v2=2gh /1+1

v=√gh

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

v=√10gh /7

Final Answer:

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.

 

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