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

Mass of the first body $m_1=5kg$ , for elastic collision e = 1

Suppose initially body $m_1$ moves with velocity u

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

$m_1{u}_1+m_2{u}_2=m_{1}v+m_2{v}_2$    Or           $5u+M\times 0=5\times \frac{u}{10}+M{v}_2$

Or             $5u=\frac{u}{2}+M{v}_2$      ……………(i)  Since, $v_1-v_2=-e\left(u_1-u_2\right)$

           $\frac{u}{10}-v_2=-1\left(u\right)$

Or       $\frac{u}{10}+u=v_2$

               $\frac{11u}{10}=v_2$                            …………(ii)

Substituting value of $v_2$  in Eq. (i) form Eq. (ii)

We get

                     $5u=\frac{u}{2}+M\left(\frac{11u}{10}\right)$    Or    $5-\frac{1}{2}=M\left(\frac{11}{10}\right)$

Or                 $M=\frac{9\times 10}{2\times 11}$         Or        $M=\frac{45}{11}$

                           = 4.09 kg