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

Options

A. `sqrt((10)/(7)gh)`
B. `sqrt((4)/(3)gh)`
C. `sqrt(gh)`
D. `sqrt((6)/(5)gh)`

Answer

A

Explanation

`mgh=(1)/(2)l omega^(2)=(1)/(2)mv^(2)`
`=(1)/(2)((2)/(5)mr^(2))omega^(2)+(1)/(2)mv^(2)=(7)/(10)mv^(2)`
`therefore v=sqrt((10)/(7)gh)`