Center of Mass, Momentum & Collision

JEE Main level, single correct, medium

9 of 130

Question 9 of 130

Two bodies are having kinetic energies in the ratio 16:9.16:9. If they have same linear momentum, the ratio of their masses respectively is:

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Answer: (B) 9:169:16

The kinetic energy and the momentum of a moving object are related by
K=p22m...(1)K=\dfrac{{p}^{2}}{2m}...\left(1\right)
Hence, the ratio of the kinetic energies of two objects having masses mm and m′m' can be calculated as follows:
KK′=p22mp22m′=m′m...(2)\begin{matrix}\dfrac{K}{{K}^{'}} & = & \dfrac{\dfrac{{p}^{2}}{2m}}{\dfrac{{p}^{2}}{2m'}} \\ & = & \dfrac{m'}{m}...\left(2\right)\end{matrix}
Substitute the ratio of the kinetic energies into equation (2) and simplify to obtain the ratio of their masses.
⇒169=m′m⇒m:m′=9:16\begin{matrix} & \Rightarrow & \dfrac{16}{9}=\dfrac{m'}{m} \\ & \Rightarrow & m:m'=9:16\end{matrix}

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