Question

Three particles of equal mass lie at distances of 1 cm, 2 cm, and 3 cm from the origin. The distance of their center of mass from the origin is

• A. 2 cm
• B. 1 cm
• C. 2.5 cm
• D. 3 cm
• E. 6 cm

Hint:

For particles with equal mass, the center of mass is simply the average of their positions.

Answer 1

The Correct Option is A

The center of mass (COM) of three particles of equal mass can be calculated using the formula: \[ x_{\text{COM}} = \frac{m_1x_1 + m_2x_2 + m_3x_3}{m_1 + m_2 + m_3} \] Since all particles have equal mass, the formula simplifies to: \[ x_{\text{COM}} = \frac{x_1 + x_2 + x_3}{3} \] Where: - \( x_1 = 1 \, \text{cm} \) - \( x_2 = 2 \, \text{cm} \) - \( x_3 = 3 \, \text{cm} \) Substituting the values: \[ x_{\text{COM}} = \frac{1 + 2 + 3}{3} = \frac{6}{3} = 2 \, \text{cm} \] Thus, the correct answer is (A) 2 cm.