Question:
Two particles of masses \(4\,\text{g}\) and \(2\,\text{g}\) are separated by a distance of \(60\,\text{cm}\). The centre of mass of the system of these two particles is
Two particles of masses \(4\,\text{g}\) and \(2\,\text{g}\) are separated by a distance of \(60\,\text{cm}\). The centre of mass of the system of these two particles is
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The centre of mass always lies closer to the heavier particle.
For two masses \(m_1\) and \(m_2\) separated by distance \(d\),
\[
x=\frac{m_2}{m_1+m_2}\,d
\]
gives the distance of the centre of mass from \(m_1\).
Updated On: Jul 9, 2026
- Lies at a distance of \(30\,\text{cm}\) from \(4\,\text{g}\) particle
- Lies at a distance of \(40\,\text{cm}\) from \(4\,\text{g}\) particle
- Lies at a distance of \(40\,\text{cm}\) from \(2\,\text{g}\) particle
Lies at a distance of \(20\,\text{cm}\) from \(2\,\text{g}\) particle
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The Correct Option is C
Solution and Explanation
Concept:
For two particles separated by a distance \(d\), the centre of mass divides the line joining them in the inverse ratio of their masses.
\[
m_1x_1=m_2x_2
\]
where \(x_1\) and \(x_2\) are the distances of the centre of mass from masses \(m_1\) and \(m_2\) respectively.
Step 1: Let the distance of the centre of mass from the \(4\,\text{g}\) particle be \(x\). Then the distance from the \(2\,\text{g}\) particle is \[ 60-x. \] Using the centre of mass condition, \[ 4x=2(60-x). \]
Step 2: Solve for \(x\). \[ 4x=120-2x. \] \[ 6x=120. \] \[ x=20\,\text{cm}. \] Thus the centre of mass is \[ 20\,\text{cm} \] from the \(4\,\text{g}\) particle.
Step 3: Find its distance from the \(2\,\text{g}\) particle. \[ 60-20=40\,\text{cm}. \] Therefore, the centre of mass lies \[ 40\,\text{cm} \] from the \(2\,\text{g}\) particle.
Step 4: Write the final answer. \[ \boxed{\text{Centre of mass lies }40\,\text{cm}\text{ from the }2\,\text{g particle}} \] \[ \boxed{\text{Answer = (C)}} \]
Step 1: Let the distance of the centre of mass from the \(4\,\text{g}\) particle be \(x\). Then the distance from the \(2\,\text{g}\) particle is \[ 60-x. \] Using the centre of mass condition, \[ 4x=2(60-x). \]
Step 2: Solve for \(x\). \[ 4x=120-2x. \] \[ 6x=120. \] \[ x=20\,\text{cm}. \] Thus the centre of mass is \[ 20\,\text{cm} \] from the \(4\,\text{g}\) particle.
Step 3: Find its distance from the \(2\,\text{g}\) particle. \[ 60-20=40\,\text{cm}. \] Therefore, the centre of mass lies \[ 40\,\text{cm} \] from the \(2\,\text{g}\) particle.
Step 4: Write the final answer. \[ \boxed{\text{Centre of mass lies }40\,\text{cm}\text{ from the }2\,\text{g particle}} \] \[ \boxed{\text{Answer = (C)}} \]
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