Question

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

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

Answer 1

Answer: (A), (C)

$ v_1 ' = \left( \frac{ m_1 - m_2 }{ m_1 + m_2 } \right) v_1 + \left( \frac{ 2 m_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 = 3 \, ms^{ - 1} $
$ v_2 ' = \left( \frac{ m_2 - m_1}{ m_2 + m_1 } \right) v_2 + \left( \frac{ 2 m_1 }{ m_2 + m_1 } \right) v_1 $
$= 0 + \left( \frac{ 2 \times 1 }{ 6 } \right) \, (3) = 1 \, ms^{ - 1} $
$ P_{ CM} = P_i = (1) (3) = 3\, kg -m/s$
$ P_5 ' = ( 5 ) (1) = 5\, kg - m / s$
$ K_{ CM} = \frac{ P_{ CM}^2 }{ 2 \, M_{ CM} } = \frac{ 9 }{ 2 \times 6 } = 0 . 75\,J$
$ K_{\text{ total} } = \frac{1}{2} \times 1 \times (3)^2 = 4 . 5\, J$