A body of mass $5 \mathrm{~kg}$ makes an elastic collision with another body at rest and continues to move in the original direction after collision with a velocity equal to $\frac{1}{10}$ th of its original velocity. Then the mass of the second body is

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Aicharya · Accepted Answer

Mass of the first body $m_1=5 \mathrm{~kg}$, for elastic collision $e=1$.

Suppose initially body $m_1$ moves with velocity $v$ after collision velocity becomes $\left(\frac{u}{10}\right)$. Let after collision velocity of $M$ block becomes $\left(v_2\right)$. By conservation of momentum $\begin{aligned} m_1 u_1+m_2 u_2 & =m_1 v_1+m_2 v_2 \\ \text { or } \quad 5 u+M \times 0 & =5 \times \frac{u}{10}+M v_2 \end{aligned}$

Since, $\begin{aligned} v_1-v_2 & =-e\left(u_1-u_2\right) \\ \frac{u}{10}-v_2 & =-1(u) \end{aligned}$ or $\quad \frac{u}{10}+u=v_2$

Substituting value of $v_2$ in Eq. (i) from Eq. (ii), we get $5 u=\frac{u}{2}+M\left(\frac{11 u}{10}\right)$ or $5-\frac{1}{2}=M\left(\frac{11}{10}\right)$ or $M=\frac{9 \times 10}{2 \times 11}$ or $\begin{aligned} M & =\frac{45}{11} \\ & =4.09 \mathrm{~kg} \end{aligned}$

A body of mass $5 \mathrm{~kg}$ makes an elastic collision with another body at rest and continues to move…

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