Concepts Of Physics MCQ Edition [Volume 1]PhysicsCentre of Mass, Linear momentum, Collision
A small body of mass m is placed over a larger mass M whose surface is horizontal near the small body and gradually curves to become vertical. The small body is pushed on the larger mass at a speed v and the system is subsequently left to itself. Assume all surfaces are frictionless. Determine the speed of the small body when it breaks off the larger mass at height h .
Options
- A[ (M^2 + m^2) (M + m)^2 v^2 - 2gh ]^ 1/2
- B[ (M^2 + Mm + m^2) (M + m)^2 v^2 - 2gh ]^ 1/2
- C[ M^2 (M + m)^2 v^2 - 2gh ]^ 1/2
- D[ m^2 (M + m)^2 v^2 - 2gh ]^ 1/2
Correct answer
B. [ (M^2 + Mm + m^2) (M + m)^2 v^2 - 2gh ]^ 1/2
Step-by-step solution
Since there are no external forces acting on the system in the horizontal direction, the horizontal component of momentum is conserved. Let V be the velocity of the larger mass M when the small body breaks off. At the point of breaking off, the surface of M is vertical, meaning the small body m has the same horizontal velocity as M . By conservation of horizontal momentum: mv = m v_x + M V Since v_x = V , we have: mv = (m + M)V V = mv m + M Let v_f be the net speed of the small body when it breaks off at height h .