Center of Mass, Momentum & Collision

JEE Main level, single correct, medium

13 of 130

Question 13 of 130

A body of mass 8kg8kg and another of mass 2kg2kg are moving with equal kinetic energy. The ratio of their respective momenta will be

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Answer: (B) 2:12:1

Given: The mass of the objects m1=8kg{m}_{1}=8kg and m2=2kg{m}_{2}=2kg.
Let the momentum of the 8kg8kg and 2kg2kg masses is p1{p}_{1} and p2{p}_{2}, respectively, then according to question, their kinetic energy are equal, i.e.,
K1=K2{K}_{1}={K}_{2}
p122m1=p222m2\dfrac{{p}_{1}^{2}}{2{m}_{1}}=\dfrac{{p}_{2}^{2}}{2{m}_{2}}
p1p2=m1m2=41=21\dfrac{{p}_{1}}{{p}_{2}}=\sqrt{\dfrac{{m}_{1}}{{m}_{2}}}=\sqrt{\dfrac{4}{1}}=\dfrac{2}{1}

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