Two bodies of masses 1m and 4m have the same KE. What is the ratio of their momenta?

2:1

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1:2

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1:4

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4:1

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Solution

The correct option is B 1:2
The relation between kinetic energy $(K)$ and momentum $(p)$ is given by, $K = \frac{p^{2}}{2 m}$ where $m$ be the mass of the body
So, $p = \sqrt{2 m K}$
Hence, $\frac{p_{1}}{p_{2}} = \frac{\sqrt{2 (m) K_{1}}}{\sqrt{2 (4 m) K_{2}}} = \sqrt{(1 / 4)} = 2 / 1$ as they have same kinetic energies so $K_{1} / K_{2} = 1$

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Two bodies of masses 1m and 4m have the same KE. What is the ratio of their momenta?

The correct option is B 1:2The relation between kinetic energy (K) and momentum (p) is given by, K=p22m where m be the mass of the bodySo, p=√2mKHence, p1p2=√2(m)K1√2(4m)K2=√(1/4)=2/1 as they have same kinetic energies so K1/K2=1