Assertion (A): A body of mass collides head on elastically with another body of mass at rest. The ratio of the final energy of the first body to the final energy of the second body is Reason (R): The collision is perfectly elastic and the coefficient

Question

Assertion (A): A body of mass $m_{1}$ collides head on elastically with another body of mass $m_{2}$ at rest. The ratio of the final energy of the first body to the final energy of the second body is $\frac{{(m_{1} - m_{2})}^{2}}{4 m_{1} m_{2}}$

Reason (R): The collision is perfectly elastic and the coefficient of restitution is 1.

Smart Achievers · Accepted Answer

(1)

${K . E .}_{1} = \frac{1}{2} m_{1} v_{1}^{2};$ ${K . E .}_{2} = \frac{1}{2} m_{2} v_{2}^{2}$

$\frac{{K . E .}_{1}}{{K . E .}_{2}} = \frac{\frac{1}{2} {(\frac{m_{1} - m_{2}}{m_{1} + m_{2}})}^{2} u_{1}^{2}}{\frac{1}{2} m_{2} {(\frac{2 m_{1}}{m_{1} + m_{2}})}^{2} u_{1}^{2}} = \frac{{(m_{1} - m_{2})}^{2}}{4 m_{1} m_{2}}$

For perfectly elastic collision, $e = 1$

Solution

1 Both (A) and (R) are true and (R) is the correct explanation of (A)

2 Both (A) & (R) are true but (R) is not correct explanation of (A)

3 (A) is true and (R) is false

4 Both (A) and (R) are false

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