Question

Two particles of masses 1 g and 2 g move towards each other with velocities 10 m/s and 20 m/s respectively. The velocity of the centre of mass of the system of the two particles is

• A. 5 m/s
• B. 10 m/s
• C. 15 m/s
• D. 20 m/s

Hint:

For systems of particles, use the center of mass velocity formula to calculate the overall motion of the system.

Answer 1

The Correct Option is A

The velocity of the center of mass \( V_{\text{cm}} \) of two particles is given by: \[ V_{\text{cm}} = \frac{m_1 v_1 + m_2 v_2}{m_1 + m_2} \] Where: - \( m_1 = 1 \, \text{g} = 0.001 \, \text{kg} \), - \( m_2 = 2 \, \text{g} = 0.002 \, \text{kg} \), - \( v_1 = 10 \, \text{m/s} \), - \( v_2 = 20 \, \text{m/s} \). Substituting the values: \[ V_{\text{cm}} = \frac{0.001 \times 10 + 0.002 \times 20}{0.001 + 0.002} = \frac{0.01 + 0.04}{0.003} = \frac{0.05}{0.003} = 5 \, \text{m/s} \] Thus, the velocity of the center of mass is \( \boxed{5 \, \text{m/s}} \).