Consider the following statements A and B and | vedclass

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(A) In a one-dimensional elastic collision between two bodies of masses $m_1$ and $m_2$ with initial velocities $u_1$ and $u_2$,the final velocities $

Vedclass · Accepted Answer

both $A$ and $B$ are true

Vedclass · Answer

(A) In a one-dimensional elastic collision between two bodies of masses $m_1$ and $m_2$ with initial velocities $u_1$ and $u_2$,the final velocities $v_1$ and $v_2$ are given by:$v_1 = \frac{m_1 - m_2}{m_1 + m_2} u_1 + \frac{2m_2}{m_1 + m_2} u_2$$v_2 = \frac{2m_1}{m_1 + m_2} u_1 + \frac{m_2 - m_1}{m_1 + m_2} u_2$For statement $A$: If $m_1 = m_2 = m$ and $u_2 = 0$,then $v_1 = 0$ and $v_2 = u_1$. This confirms that the first body comes to rest and the second moves with the initial velocity of the first.For statement $B$: If $m_1 = m_2 = m$,the equations become $v_1 = u_2$ and $v_2 = u_1$. This confirms that the bodies exchange their velocities.Therefore,both statements $A$ and $B$ are true.

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