Question

Assertion :In a two-body collision, the momenta of the particles are equal and opposite to one another, before as well as after the collision when measured in the centre of mass frame. Reason: The momentum of the system is zero from the centre of mass frame.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

In center of mass frame, $COM$ remains at rest i.e $V_{CM}=0$

$⟹$ Momentum of the system is zero in centre of mass frame.

Using $V_{CM}=\frac{m_1{v}_1+m_2{v}_2}{M}$

$0=\frac{m_1{v}_1+m_2{v}_2}{M}$

$⟹m_1{v}_1=-m_2{v}_2$ OR $\overrightarrow{p_1}=-\overrightarrow{p_2}$

Hence in COM frame, momenta of both particles must be equal and opposite to one another.

Thus both the statements are true and Reason explains the Assertion very well.