A solid sphere of mass 2 kg rolls on a smooth horizontal surface at 10 ~m / s and then rolls up a smooth 30^ incline. The maximum height reached by the sphere is (g=9.8 ~m / s ^2 )

Step-by-step solution

Applying conservation of mechanical energy, we can write 1 2 I ^2+ 1 2 m v^2=m g h where, h is maximum height reached by the sphere, v is linear velocity and is angular velocity of the sphere. 1 2 I ( v r )^2+ 1 2 m v^2=m g h [ v= r] aligned & 1 2 2 5 m r^2 v^2 r^2 + 1 2 m v^2=m g h & 1 5 m v^2+ 1 2 m v^2=m g h & 7 10 m v^2=m g h & h= 7 10 v^2 g = 7 10 10^2 9.8 = 70 9.8 &= 100 14 = 50 7 =7.1 ~m aligned