A smooth sphere of mass M moving with velocity u directly collides elastically with another sphere of mass m at rest. After the collision, their final velocities are V and v respectively. Then v is

Question

A smooth sphere of mass M moving with velocity u directly collides elastically with another sphere of mass m at rest. After the collision, their final velocities are V and v respectively. Then v is, 2 uM m, 2 um M, 2 u 1 + m M, 2 u 1 + M m

MARKS App · Accepted Answer

By law of conservation of momentum, Mu = MV + mv …(i) e = | v 1 − v 2 | | u 1 − u 2 | = v - V u ⇒ e = 1 = v - V u ⇒ u = v - V ⇒ Mu = Mv − MV ....(ii) From (i) and (ii), 2 Mu = ( M + m ) v ⇒ v = 2 uM M + m ⇒ v = 2 u 1 + m M

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