A small block of mass m is placed on a smooth body of mass M; the combination is placed on a smooth horizontal surface and are given velocities u towards each other as shown in the diagram. The maximu

Question

A small block of mass m is placed on a smooth body of mass M; the combination is placed on a smooth horizontal surface and are given velocities u towards each other as shown in the diagram. The maximum height to which the small block of mass m rises after breaking off the vertical section of the body of mass M is H, relative to its initial level. Assume M > m.

TestHub · Accepted Answer

Momentum: M u − m u = ( M + m ) v ⇒ v = M + m M − m ​ u - (C) correct. Energy: m g H = 2 1 ​ ( M + m ) ( u 2 − v 2 ) = M + m 2 M m ​ u 2 , so u 2 = 2 M ( M + m ) g H ​ > 2 g H ​ - (A) wrong; the raising work is only m g H  = 4 × 2 1 ​ M u 2 - (B) wrong. KE at the highest point: 2 1 ​ ( M + m ) v 2 = 4 M ( M − m ) 2 g H ​ - (D) correct. Ans. (C,D)

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