A solid sphere of mass 2 kg and radius R rolls on a smooth horizontal surface at `5 ms^(-1)` and then rolls up on a smooth inclined plane of inclination angle `30^(@)` with horizontal. Calculate the height (in m ) attained by the sphere before it stops.(Take `g= 10 m s^(-2))`

Answer

`1.75`

Explanation

`(K.E.) _("Rolling") = (P.E.) ` at .h.
`(1)/(2) Mv ^(2) + (1)/(2) I omega ^(2) = Mgh`
`(1)/(2) Mv ^(2) + (1)/(2) ((2)/(5) MR ^(2)) ((v ^(2))/( R ^(2))) = Mgh`
`(7)/(10) Mv ^(2) = Mgh`
`h = ( 7v ^(2))/( 10 g ) = ( 7 (5) ^(2))/( 10 (10)) = 1. 75 m`