Work Energy Power

JEE Main level, single correct, medium

63 of 183

Question 63 of 183

Two bodies of mass 4g4g and 25g25g are moving with equal kinetic energies. The ratio of magnitude of their linear momentum is :

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Answer: (C) 2:52:5

The kinetic energy (K)\left(K\right) of an object is given by
K=12mv2=p22m...(1)\begin{matrix}K & = & \dfrac{1}{2}m{v}^{2} \\ & = & \dfrac{{p}^{2}}{2m}...\left(1\right)\end{matrix}
Following equation (1), for the two given bodies, it can be written that
p122m1=p222m2⇒p1p2=m1m2=425=25\dfrac{{p}_{1}^{2}}{2{m}_{1}}=\dfrac{{p}_{2}^{2}}{2{m}_{2}} \Rightarrow \dfrac{{p}_{1}}{{p}_{2}}=\sqrt{\dfrac{{m}_{1}}{{m}_{2}}} =\sqrt{\dfrac{4}{25}} =\dfrac{2}{5}

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