Question

Two bodies of masses \( M \) and \( 4M \) initially at rest, start moving towards each other due to their mutual attraction. The velocity of their centre of mass when the first body attains a velocity \( v_0 \) is

• A. zero
• B. \( -v_0 \)
• C. \( 2v_0 \)
• D. \( -4v_0 \)

Hint:

In an isolated system with no external force, the center of mass either remains at rest or moves with constant velocity, regardless of internal interactions.

Answer 1

The Correct Option is A

Step 1: Initially, both masses are at rest, so the total momentum of the system is zero. Step 2: Since no external force is acting on the system, the velocity of the center of mass (CM) remains constant. Step 3: If it starts from rest, the center of mass continues to be at rest. Hence, regardless of the motion of the individual particles due to internal forces (mutual attraction), the center of mass velocity remains: \[ v_{\text{CM}} = 0 \] % Final Answer \[ \boxed{0} \]