A spherical rigid ball is released from rest and starts rolling down an inclined plane from height h = 7 m , as shown in the figure. It hits a block at rest on the horizontal plane (assume elastic collision). If the mass of both the ball and the block is m and the ball is rolling without sliding, then the speed of the block after collision is close to

Step-by-step solution

As collision is elastic and masses of colliding objects are equal, so there is exchange of total energy of moving mass to stationary mass. Hence, velocity of block = velocity of sphere just before collision. For sphere, if v = velocity of translation of centre of mass at the bottom of plane and ω = angular speed, then by energy conservation, we have m g h = 1 2 m v 2 + 1 2 I ω 2 Here, ω = v R and I = 2 5 m R 2 Substituting and solving for velocity, we have v = 10 7 g h = 10 × 10 × 7 7 = 10 m / s ∴ Velocity of block