Assertion :Two bodies of different masses have same kinetic energies. Their momenta are in the direct ratio of their masses. Reason: $p = m v$

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is incorrect but Reason is correct

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Both Assertion and Reason are incorrect

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Solution

The correct option is C Assertion is incorrect but Reason is correct
Given that,
$\frac{1}{2} m_{1} v_{1}^{2} = \frac{1}{2} m_{2} v_{2}^{2}$ ...(equation 1)
$⟹ {(\frac{v_{1}}{v_{2}})}^{2} = \frac{m_{2}}{m_{1}} ⟹ \frac{v_{1}}{v_{2}} = \sqrt{\frac{m_{2}}{m_{1}}}$ ...(equation 2)
By equation 1 and 2,
$\frac{m_{1} v_{1}}{m_{2} v_{2}} = \frac{v_{2}}{v_{1}} = \sqrt{\frac{m_{1}}{m_{2}}}$

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Assertion :Two bodies of different masses have same kinetic energies. Their momenta are in the direct ratio of their masses. Reason: p=mv

The correct option is C Assertion is incorrect but Reason is correctGiven that,12m1v21=12m2v22 ...(equation 1)⟹(v1v2)2=m2m1⟹v1v2=√m2m1 ...(equation 2)By equation 1 and 2,m1v1m2v2=v2v1=√m1m2

Assertion :Two bodies of different masses have same kinetic energies. Their momenta are in the direct ratio of their masses. Reason: $p = m v$