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The following bodies are made to roll up...

The following bodies are made to roll up (without slipping) the same inclined plane from a horizontal plane : (i) a ring of radius R, (ii) a solid cylinder of radius `R/2` and (iii) a solid sphere of radius `R/4` If, in each case, the speed of the center of mass at the bottom of the incline is same, the ratio of the maximum heights they climb is

A

`14:15:20`

B

`10:15:7`

C

`4:3:2`

D

`20:15:14`

Text Solution

Verified by Experts

The correct Answer is:
D
`mgh=(1)/(2)mv^(2)(1+k)`
`h_(1):h_(2):h_(3)=1+k_(1):1+k_(2):1+k_(3)`
`h_(1):h_(2):h_(3)=1+1:1+1//2:1+2//5`
`h_(1):h_(2):h_(3)=2:3//2:7//5`
`h_(1):h_(2):h_(3)=20:15:14`
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