Center of Mass, Momentum & Collision

JEE Main level, single correct, medium

109 of 130

Question 109 of 130

A particle of mass mm with an initial velocity ui^u\hat{i} collides perfectly elastically with a mass 3m3m at rest. It moves with a velocity vj^v\hat{j} after collision, then, vv is given by

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Answer: (C) v=u2v=\dfrac{u}{\sqrt{2}}

From momentum conservation
mui^+0=mvj^+3mv⃗′mu\hat{i}+0=mv\hat{j}+3m{\vec{v}}^{'}
v⃗′=u3i^−v3j^{\vec{v}}^{'}=\dfrac{u}{3}\hat{i}-\dfrac{v}{3}\hat{j}
From kinetic energy conservation 12mu2=12mv2+12(3m)((u3)2+(v3)2)\dfrac{1}{2}m{u}^{2}=\dfrac{1}{2}m{v}^{2}+\dfrac{1}{2}(3m)\left({\left(\dfrac{u}{3}\right)}^{2}+{\left(\dfrac{v}{3}\right)}^{2}\right)
solving v=u2v=\dfrac{u}{\sqrt{2}}

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