Question

A point mass of $1\text{kg}$ collides elastically with a stationary point mass of $5\text{kg}$. After their collision, the $1\text{kg}$ mass reverses its direction and moves with a speed of $2\text{m/s}$. Which of the following statements is (are) correct for the system of two masses ?

• A. Total momentum of the system is $7{\text{kg ms}}^{-1}$.
• B. Momentum of $5\text{kg}$ mass after collision is $5{\text{kg ms}}^{-1}$.
• C. Velocity of $5\text{kg}$ after collision is $1\text{m/s}$.
• D. Velocity of $1\text{kg}$ before collision is $2\text{m/s}$.

Answer 1

Answer: (B), (C)

Velocity of $5\text{kg}$ after collision is $1\text{m/s}$.

Let initial velocity of $1\text{kg}$ mass be $u$ and final velocity of $5\text{kg}$ mass be $v$.


Applying conservation of linear momentum, taking rightward positive
$m_1{u}_1+m_2{u}_2=m_1{v}_1+m_2{v}_2$
$1\times u+0=1\times (-2)+5v$
$\Rightarrow u+2=5v$ ...(i)

Now $e=1=\frac{v_{separation}}{v_{approach}}$
$\Rightarrow \frac{v-(-2)}{u-0}=1\Rightarrow v+2=u$ ...(ii)

Solving (i) and (ii),
$v=1\text{m/s}$ & $u=3\text{m/s}$
Momentum of $5\text{kg}$ mass after collsion $=5v=5\text{kg m/s}$
Also, total momentum of system $=m_1{u}_1+m_2{u}_2$
$=1\times 3+0=3\text{kg m/s}$