Two bodies are having kinetic energies in the ratio 16 : 9. If they have same linear momentum, the ratio of their masses respectively is [2023]

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Solution

Q.
Two bodies are having kinetic energies in the ratio 16 : 9. If they have same linear momentum, the ratio of their masses respectively is [2023]

1 4 : 3

2 3 : 4

3 16 : 9

4 9 : 16

Ans.
(4)

$\frac{K_{1}}{K_{2}} = \frac{p_{1}^{2}}{2 m_{1}} \times \frac{2 m_{2}}{p_{2}^{2}} = \frac{m_{2}}{m_{1}} = \frac{16}{9}$

$\frac{m_{1}}{m_{2}} = \frac{9}{16}$

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