Question

The X and Y coordinates of the three particles of masses m, 2m and 3m are respectively (0,0), (1,0) and (-2,0). The X-coordinate of the centre of mass of the system is

• A. $\frac 1{3} $
• B. $\frac 2{3} $
• C. $\frac -1{3} $
• D. $\frac -2{3} $
• E. $\frac 1{6} $

Answer 1

The Correct Option is D

We are given the positions and masses of three particles: 

• Particle 1 has mass \( m \) at position \( (0,0) \)
• Particle 2 has mass \( 2m \) at position \( (1,0) \)
• Particle 3 has mass \( 3m \) at position \( (-2,0) \)

The x-coordinate of the center of mass of the system is given by the formula: \[ x_{\text{cm}} = \frac{\sum m_i x_i}{\sum m_i} \] Where: - \( m_i \) is the mass of each particle, - \( x_i \) is the x-coordinate of each particle. Substituting the given values: \[ x_{\text{cm}} = \frac{m \cdot 0 + 2m \cdot 1 + 3m \cdot (-2)}{m + 2m + 3m} \] Simplifying: \[ x_{\text{cm}} = \frac{0 + 2m - 6m}{6m} = \frac{-4m}{6m} = \frac{-2}{3} \] Thus, the x-coordinate of the center of mass is \( \frac{-2}{3} \).

Correct Answer:

Correct Answer: (D) \( \frac{-2}{3} \)