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The speed of a homogeneous solid sphere ...

The speed of a homogeneous solid sphere after rolling down an inclined plane of vertical height `h` from rest without slipping will be.

A

`sqrt((10 gh)/(7))`

B

`sqrt((6gh)/(5))`

C

`sqrt((4 gh)/(5))`

D

`sqrt(2gh)`

Text Solution

Verified by Experts

The correct Answer is:
B
In pure rolling, mechanical energy remains conserved.
Therefore, at bottomost post, total kinetic energy will be `mgh`
Ratio of rotational to translational kinetic energy will be `(2)/(3)`
`:. K_(T)=(3)/(5)(mgh)rArr(3)/(5)mgh=(1)/(2)mv^(2)`
`:.` The speed of a uniform spherical shell
`v=sqrt((6gh)/(5))`.
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