Question

Two bodies A and B of masses 80 g and 120 g move with same speed, $6~cm~s^{-1}$ in a plane. The speed of the centre of mass of the system is

• A. $6.2~cm~s^{-1}$
• B. $6.0~cm~s^{-1}$
• C. $2.4~cm~s^{-1}$
• D. $2.0~cm~s^{-1}$
• E. $3.2~cm~s^{-1}$

Hint:

If all particles in a system are moving with the exact same velocity $\vec{v}$, then the centre of mass MUST also be moving with that same velocity $\vec{v}$. You don't even need to perform the calculation!

Answer 1

The Correct Option is B

Concept:
Physics - Velocity of the Centre of Mass ($v_{cm}$).
For a system of two particles moving in the same direction, $v_{cm} = \frac{m_1v_1 + m_2v_2}{m_1 + m_2}$.
Step 1: Identify the given values.

• Mass $m_A = 80$ g
• Mass $m_B = 120$ g
• Speed $v_A = 6~cm~s^{-1}$
• Speed $v_B = 6~cm~s^{-1}$

Step 2: Apply the formula for the velocity of the centre of mass.
$$ v_{cm} = \frac{(80 \times 6) + (120 \times 6)}{80 + 120} $$
Step 3: Simplify the calculation.
Factor out the common speed (6): $$ v_{cm} = \frac{6 \times (80 + 120)}{80 + 120} $$ $$ v_{cm} = \frac{6 \times 200}{200} $$
Step 4: Solve for $v_{cm}$.
$$ v_{cm} = 6~cm~s^{-1} $$ The speed of the centre of mass remains $6.0~cm~s^{-1}$.