question_answer

A particle of mass m moving in the x direction with speed 2v is hit by another particle of mass 2m moving in the y direction with speed v. If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to: [JEE MAIN 2015]

A) 56 %

B) 62 %

C) 44 %

D) 50 %

Correct Answer: A

Solution :

[a]along x-axis

\[2m(2v)=3.{{v}_{x}}\Rightarrow {{v}_{x}}=\frac{2v}{3}\]

\[2m(v)=3m{{v}_{y}}\Rightarrow {{v}_{y}}=\frac{2v}{3}\]

\[{{v}_{net}}=\sqrt{v_{x}^{v}+u_{y}^{v}}=\frac{2\sqrt{2}v}{3}\]

1144

\[=\frac{1}{2}m{{(2v)}^{2}}+\frac{1}{2}\left( 2m \right){{v}^{2}}-\frac{1}{2}\left( 3m \right){{\left( \frac{2\sqrt{2}}{3} \right)}^{2}}\]AO IIT ACADEMY / JEE - MAIN EXAM - 2015 / QP + Solutions / \[=3m{{v}^{2}}-\frac{4m{{v}^{2}}}{3}=\frac{5m{{v}^{2}}}{2}\]

\[=\frac{loss\,in\,K.E}{Initial\,K.E}\times 100\]

\[=\frac{5/3m{{v}^{2}}}{3m{{v}^{2}}}\times 100=5/9\times 100=56%\]D