A body of mass m moving with velocity v makes | vedclass

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(C) For a perfectly elastic head-on collision,the final velocity $v_1$ of the first body (mass $m_1$) is given by $v_1 = \left( \frac{m_1 - m_2}{m_1 +

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$\frac{8}{9}$ of its initial kinetic energy

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(C) For a perfectly elastic head-on collision,the final velocity $v_1$ of the first body (mass $m_1$) is given by $v_1 = \left( \frac{m_1 - m_2}{m_1 + m_2} \right) v$. Here,$m_1 = m$ and $m_2 = 2m$. Substituting these values: $v_1 = \left( \frac{m - 2m}{m + 2m} \right) v = \left( \frac{-m}{3m} \right) v = -\frac{v}{3}$. The initial kinetic energy is $K_i = \frac{1}{2}mv^2$. The final kinetic energy of the first body is $K_f = \frac{1}{2}m(v_1)^2 = \frac{1}{2}m(-\frac{v}{3})^2 = \frac{1}{2}m(\frac{v^2}{9}) = \frac{1}{9} K_i$. The loss in kinetic energy is $\Delta K = K_i - K_f = K_i - \frac{1}{9} K_i = \frac{8}{9} K_i$. Thus,the loss of kinetic energy is $\frac{8}{9}$ of its initial kinetic energy.

$A$ body of mass $m$ moving with velocity $v$ makes a head-on elastic collision with another body of mass $2m$ which is initially at rest. The loss of kinetic energy of the colliding body (mass $m$) is:

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