A sphere of mass m and radius r rolls on a horizontal plane without slipping with the speed u . Now if it rolls up vertically , the maximum height it would attain will be

Options

A. `3u^(2) //4 g`
B. `5u^(2) //2g`
C. `7u^(2) // 10g `
D. `u^(2)//2g`

Answer

C

Explanation

The rolling sphere has rotational as well as translational kinetic energy .
`therefore` Kinetic energy = `(1)/(2) "mu"^(2) + (1)/(2) I omega^(2)`
`= (1)/(2)"mu"^(2) + (1)/(2) ((2)/(5) mr^(2)) omega^(2) = (1)/(2) "mu"^(2) + ("mu"^(2))/(5) = (7)/(10) "mu"^(2)` .
Potential energy = kineti energy
`therefore mgh = (7)/(10) "mu"^(2) or h = (7u^(2))/(10 g)`