Question

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 equal to 1/10th 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

Answer 1

The correct option is A 4.09 kg

Mass of the first body $m_1=5$ kg, for elastic collision e = 1.
Suppose initially body$m_1$ moves with velocity v after collision velocity becomes $\frac{u}{10}$
Let after collision velocity of M block becomes $\left(v_2\right)$.
By conservation of momentum
$m_1{u}_1+m_2{u}_2=m_1{v}_1+m_2{v}_2$
or 5u + M 0 = 5 $\frac{u}{10}$ + $M{v}_2$
or 5u = $\frac{u}{2}$+ $M{v}_2$ . (i)
Since, $v_1-v_2=-e(u_1-u_2)$
$\frac{u}{10}-v_2=-u$
Or $\frac{u}{10}+u=v_2$
$\frac{11u}{10}=v_2$
Substituting value of $v_2$ in Eq. (i) from Eq. (ii). we get
$5u=\frac{u}{2}+M\frac{11u}{10}$
Or $5-\frac{1}{2}=M\frac{11}{10}$
Or M = $\frac{9\times 10}{2\times 11}$
Or M = $\frac{45}{11}$ = 4.09 kg