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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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4.09 kg
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 $\begin{aligned}
M & =\frac{45}{11} \\
& =4.09 \mathrm{~kg}
\end{aligned}$

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 $\begin{aligned}
M & =\frac{45}{11} \\
& =4.09 \mathrm{~kg}
\end{aligned}$
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