Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

Three particles of masses \( m \), \( 2m \), and \( 3m \) are placed on the \( x \)-axis at positions \( x = 0 \), \( x = L \), and \( x = 2L \) respectively. A fourth particle of mass \( 4m \) is added at position \( x = x_4 \) such that the centre of mass of the four-particle system shifts to \( x = L \). The coordinate \( x_4 \) must be:

1. A
   \( \frac{1}{2}L \)
2. B
   \( \frac{3}{4}L \)
3. C
   \( L \)
4. D
   \( \frac{5}{4}L \)