Q64 / 90 · JEE Main 2022 (26 Jul Shift 2) · Physics

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

A
$1 : 1$
Correct answer
B
$2 : 1$
C
$1 : 4$
D
$4 : 1$

Solution

Given: The mass of the objects $m_{1} = 8 kg$ and $m_{2} = 2 kg$ .
Let the momentum of the $8 kg$ and $2 kg$ masses is $p_{1}$ and $p_{2}$ , respectively, then according to question, their kinetic energy are equal, i.e.,
$K_{1} = K_{2}$
$\frac{p_{1}^{2}}{2 m_{1}} = \frac{p_{2}^{2}}{2 m_{2}}$
$\frac{p_{1}}{p_{2}} = \sqrt{\frac{m_{1}}{m_{2}}} = \sqrt{\frac{4}{1}} = \frac{2}{1}$

Hence, the correct answer is option: 'B'.

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

Solution

Relevant Questions

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