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Q.

Two bodies of masses 2m and m have their kinetic energy in the ratio $8 : 1$ ,then the ratio of their linear momenta is

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a

$8 : 1$

b

$1 : 8$

c

$4 : 1$

d

$1 : 4$

answer is D.

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Detailed Solution

$G i v e n t h a t m_{1} = 2 m, m_{2} = m, K_{1} K_{2} = 8 : 1 p_{1} : p_{2} = ? W e k n o w p = \sqrt{2 m K} \frac{P_{1}}{P_{2}} = \frac{\sqrt{2 m_{1} K_{1}}}{\sqrt{2 m_{2} K_{2}}} = \sqrt{\frac{2 \times 2 m \times 8}{2 \times m \times 1}} = 4 ∴ p_{1} : p_{2} = 4 : 1$

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Two bodies of masses 2m and m have their kinetic energy in the ratio 8:1 ,then the ratio of their linear momenta is