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Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
हिन्दीThree 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:
Correct answer · Option 1
\( \frac{1}{2}L \)
Explanation
\( X_{\text{cm}} = \frac{m(0) + 2m(L) + 3m(2L) + 4m(x_4)}{10m} = L \implies 8mL + 4mx_4 = 10mL \implies 4x_4 = 2L \implies x_4 = \frac{L}{2} \).
