Question

A body of mass $5kg$ 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

• A. 4.09 kg
• B. 0.5 kg
• C. 5 kg
• D. 5.09 kg

Answer 1

Answer: (A)

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

Let 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 $(v_2)$ .
By conservation of momentum
$m_1{u}_1+m_2{u}_2=m_1{v}_1+m_2{v}_2$
or $5u+M\times 0=5\times \frac{u}{10}+M{v}_2$
or $5u=\frac{u}{3}+M{v}_2$ ....(i)
Since , $v_1-v_2=-e(u_1-u_2)$
or $\frac{u}{10}-v_2=-1(u)$ or $\frac{u}{10}+u=v_2$
or $\frac{11u}{10}=v_2$ ......(ii)
Substituting value of $v_2$ in Eq. (i) from Eq. (ii)
$5u=\frac{u}{2}+M\left(\frac{11u}{10}\right)$
or $5-\frac{1}{2}=M\left(\frac{11}{10}\right)$
$\Rightarrow M=\frac{9\times 10}{2\times 11}=\frac{45}{11}$
$=4.09kg$