A mass of 400g and a mass of 100g have same KE, then the ratio of their momentums will be

2:1

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1:2

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1:3

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3:1

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Solution

The correct option is A 2:1
$\frac{P_{1}}{P_{2}} = \sqrt{\frac{2 m_{1} E_{1}}{2 m_{2} E_{2}}} = \sqrt{\frac{2 m_{1}}{2 m_{2}}} [A s E_{1} = E_{2}]$
We have
$\frac{P_{1}}{P_{2}} = \sqrt{\frac{2 m_{1}}{2 m_{2}}} = \sqrt{\frac{m_{1}}{m_{2}}}$
$∴ \frac{P_{2}}{P_{1}} = \sqrt{\frac{m_{2}}{m_{1}}}$
Here, $m_{2} = 400 g, m_{1} = 100 g$
$∴ \frac{P_{2}}{P_{1}} = \sqrt{\frac{400}{100}} = \frac{\sqrt{4}}{1} = \frac{2}{1}$
$\Rightarrow P_{2} : P_{1} = 2 : 1$

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A mass of 400g and a mass of 100g have same KE, then the ratio of their momentums will be

The correct option is A 2:1P1P2=√2m1E12m2E2=√2m12m2[AsE1=E2]We haveP1P2=√2m12m2=√m1m2∴P2P1=√m2m1Here, m2=400g,m1=100g∴P2P1=√400100=√41=21⇒P2:P1=2:1