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Two bodies with kinetic energies in the ratio 4:1 are moving with equal linear momentum. The ratio of their masses is

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a

$4 : 1$

b

$1 : 2$

c

$1 : 1$

d

$1 : 4$

answer is D.

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Detailed Solution

$K_{1} : K_{2} = 4 : 1, p_{1} = p_{2}, m_{1} : m_{2} = ? ∴ \frac{K_{1}}{K_{2}} = \frac{m_{2}}{m_{1}} \Rightarrow \frac{m_{2}}{m_{1}} = \frac{4}{1} K_{1} = \frac{{p_{1}}^{2}}{2 m_{1}}, K_{2} = \frac{{p_{2}}^{2}}{2 m_{2}} \frac{K_{1}}{K_{2}} = \frac{p^{2}}{2 m_{1}} \times \frac{2 m_{2}}{p^{2}} ∴ P_{1} = P_{2} = P \frac{K_{1}}{K_{2}} = \frac{m_{2}}{m_{1}} = \frac{4}{1} \Rightarrow \frac{4}{1} ∴ m_{1} : m_{2} = 1 : 4$

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