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

• A. Lies at a distance of \(30\,\text{cm}\) from \(4\,\text{g}\) particle
• B. Lies at a distance of \(40\,\text{cm}\) from \(4\,\text{g}\) particle
• C. Lies at a distance of \(40\,\text{cm}\) from \(2\,\text{g}\) particle
• D. Lies at a distance of \(20\,\text{cm}\) from \(2\,\text{g}\) particle

Hint:

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 \(m_1\).

Answer 1

The Correct Option is C

Concept: Centre of mass from 4g: \(4x = 2(60-x) \Rightarrow 4x = 120 - 2x \Rightarrow 6x = 120 \Rightarrow x = 20\) cm. From 2g: \(60-20 = 40\) cm.

Step 1: Write the final answer. \(\boxed{\text{40 cm from the 2 g particle}}\)