Question:
Two objects P and Q initially at rest move towards each other under mutual force of attraction. At the instant when the velocity of P is \(v\) and that of Q is \(2v\), the velocity of centre of mass of the system is
Two objects P and Q initially at rest move towards each other under mutual force of attraction. At the instant when the velocity of P is \(v\) and that of Q is \(2v\), the velocity of centre of mass of the system is
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If no external force acts, centre of mass velocity remains constant.
Updated On: May 8, 2026
- \(v\)
- \(3v\)
- \(2v\)
- \(1.5v\)
- zero
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The Correct Option is
Solution and Explanation
Concept:
If only internal forces act on a system, then total momentum remains conserved. Hence, centre of mass velocity remains constant.
Step 1: Initial condition. Initially both are at rest: \[ \text{Total momentum} = 0 \]
Step 2: At later instant. Let masses be \(m_1, m_2\). Then: \[ m_1 v = m_2 (2v) \] Momentum in opposite directions cancel each other.
Step 3: Total momentum remains zero. \[ P_{\text{total}} = 0 \]
Step 4: Velocity of centre of mass. \[ V_{cm} = \frac{P_{\text{total}}}{m_1 + m_2} = 0 \]
Step 5: Conclusion. \[ \boxed{0} \]
Step 1: Initial condition. Initially both are at rest: \[ \text{Total momentum} = 0 \]
Step 2: At later instant. Let masses be \(m_1, m_2\). Then: \[ m_1 v = m_2 (2v) \] Momentum in opposite directions cancel each other.
Step 3: Total momentum remains zero. \[ P_{\text{total}} = 0 \]
Step 4: Velocity of centre of mass. \[ V_{cm} = \frac{P_{\text{total}}}{m_1 + m_2} = 0 \]
Step 5: Conclusion. \[ \boxed{0} \]
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