Concepts Of Physics MCQ Edition [Volume 1]PhysicsCentre of Mass, Linear momentum, Collision
A railroad car of mass M initially rests on frictionless rails. A man of mass m starts moving towards the engine on the car. If the car recoils backward along the rails with a speed v , determine the velocity at which the man approaches the engine.
Options
- A(1 + m M )v
- B( m M )v
- C( M m )v
- D(1 + M m )v
Correct answer
D. (1 + M m )v
Step-by-step solution
Let the velocity of the man relative to the ground be v_m and the velocity of the car relative to the ground be v_c = -v . Since no external horizontal force acts on the system, the total linear momentum is conserved. m v_m + M v_c = 0 m v_m - M v = 0 v_m = M m v The velocity at which the man approaches the engine is his velocity relative to the car. v_ rel = v_m - v_c v_ rel = M m v - (-v) v_ rel = (1 + M m ) v