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 ~ . 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 4kg $ 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

The Correct Option is C

$ v_1 ' = \bigg( \frac{ m_1 - m_2 }{ m_1 + m_2 } \bigg) v_1 + \bigg( \frac{ 2 m_2 }{ m_1 + m_2 } \bigg) v_2 $
- 2 = $ \bigg( \frac{ 1 - 5 }{ 1 + 5 }\bigg) v_1 + 0 $ $ \hspace20mm$ $ (as \, v_2 = 0 )$
$\therefore v_1 = 3 \, ms^{ - 1} $
$ v_2 ' = \bigg( \frac{ m_2 - m_1}{ m_2 + m_1 } \bigg) v_2 + \bigg( \frac{ 2 m_1 }{ m_2 + m_1 } \bigg) v_1 $
= 0 + $ \bigg( \frac{ 2 \times 1 }{ 6 } \bigg) \, (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_{ total } = \frac{1}{2} \times 1 \times (3)^2 = 4 . 5 $ J
$\therefore$ Correct options are (a) and (c)