Two bodies of masses M and m ( M m ) are attached to the two ends of a light inextensible string passing over a frictionless pulley. The system is held at rest with the string taut and vertical with

Question

Two bodies of masses M and m ( M > m ) are attached to the two ends of a light inextensible string passing over a frictionless pulley. The system is held at rest with the string taut and vertical with both masses at a height 'd' above an inelastic table. The system is now released. Calculate the height to which the larger mass will rise after it has hit the table.

TestHub · Accepted Answer

M lands with v 2 = M + m 2 ( M − m ) g d ​ (Atwood over d). The table is inelastic, so M stops; m rises, falls back and jerks the string taut with speed v downward. Jerk (momentum): m v = ( M + m ) v ′ ⇒ v ′ = M + m m v ​ , and M starts upward at v ′ . Retardation = M + m ( M − m ) g ​ ; height = 2 a v ′2 ​ = 2 ( M + m ) ( M − m ) g m 2 v 2 ​ = ( M + m m ​ ) 2 d . Answer: (D)

Physics - Center of Mass Question with Solution | TestHub

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