A uniform solid spherical ball is rolling down a smooth inclined plane from a height h . The velocity attained by the ball when it reaches the bottom of the inclined plane is v. If the ball is now thrown vertically upwards with the same velocity v , the maximum height to which the ball will rise is

Step-by-step solution

We know that total kinetic energy of a body rolling without slipping K_ total =K_ rot +K_ trans For solid spherical ball, I= 2 5 m R² (along to diameter) and v=R where R is radius of spherical ball So. K_ total = 1 2 ( 2 5 m R² ) ²+ 1 2 m R² ² array l = 7 10 m R² ² K= 7 10 m v² array Potential energy = Kinetic energy aligned m g h &= 7 10 m v² v² &= 10 7 g h aligned For vertical projection, array c v²=u²+2 g h^ 10 7 g h=0+2 g h^ h^ = 5 7 h array