Question

A point mass of $1kg$ collides elastically with a stationary point mass of $5kg.$ After their collision, the $1kg$ mass reverses 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 $5kg$ mass after collision is $4kgm{s}^{-1}$
• C. Kinetic energy of the centre of mass is $0.75J$
• D. Total kinetic energy of the system is $4J$

Answer 1

Answer: (A), (C)

$v_1^{\prime }=\left(\frac{m_1-m_2}{m_1+m_2}\right)v_1+\left(\frac{2m_2}{m_1+m_2}\right)v_2$
$-2=\left(\frac{1-5}{1+5}\right)v_1+0$ (as $v_2=0$ )
$\therefore v_1=3m{s}^{-1}$
$v_2^{\prime }=\left(\frac{m_2-m_1}{m_2+m_1}\right)v_2+\left(\frac{2m_1}{m_2+m_1}\right)v_1$
$=0+\left(\frac{2\times 1}{6}\right)(3)=1m{s}^{-1}$
$P_{CM}=P_i=(1)(3)=3kg-m/s$
$P_5^{\prime }=(5)(1)=5kg-m/s$
$K_{CM}=\frac{P_{CM}^2}{2M_{CM}}=\frac{9}{2\times 6}=0.75J$
$K_{\text{ total}}=\frac{1}{2}\times 1\times (3{)}^2=4.5J$