Question

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

• A. Total momentum of the system is $3kgm{s}^{-1}$
• B. Momentum of 5 kg mass after collision is $4kgm{s}^{-1}$
• C. Kinetic energy of the centre of mass is $0.75J$
• D. To kinetic energy of the system is $4J$

Answer 1

The correct option is C Kinetic energy of the centre of mass is $0.75J$

Applying conservation of linear momentum

$1\times v+5\times 0=-1\times 2v_2$……$\left(1\right)$

As collision is elastic

$v_2+2=v$

$v_2=1m{s}^{-1}$

$v=3m{s}^{-1}$

Total momentum of the system

$=3kgm{s}^{-1}$

$v_{cm}=\frac{1\times v+0}{1+5}$

_{$=\frac{1}{2}m/s$}

K.E=$=\frac{1}{2}(1+2){v^2}_{cm}=0.75j$

Hence C is correct ans.