A uniform solid sphere of radius `R`, rolling without sliding on a horizontal surface with an angular velocity `omega_(0)`, meets a rough inclined plane of inclination `theta = 60^@`. The sphere starts pure rolling up the plane with an angular velocity `omega` Find the value of `omega`.

Answer

`9/14omega_(0)`

Explanation

Using the conservation of angular momentum about the point of contact with the inclined plane.

`2/5mR^(2)omega_(0)+mv_(0)Rcos60^(2)=7/5mR^(2)omega`
`2/5 mR^(2)omega_(0)+(momega_(0)R^(2))/2=7/5mR^(2)omega`
`9/10 mR^(2)omega_(0)=7/5mR^(2)omega`
`:. omega=9/14omega_(0)`