OnlineCBT
Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
हिन्दीThree particles each of mass \( 2\text{ kg} \) are placed at points \( (1, 2) \), \( (3, 4) \), and \( (5, 6) \) in the \( xy \)-plane. A fourth particle of mass \( M \) is added at \( (-3, -4) \) such that the centre of mass of the system lies at the origin \( (0,0) \). The mass \( M \) must be:
Correct answer · Option 2
\( 6\text{ kg} \)
Explanation
\( \sum m_i x_i = 2(1) + 2(3) + 2(5) + M(-3) = 0 \implies 2+6+10 - 3M = 0 \implies 18 = 3M \implies M = 6\text{ kg} \). Check y: \( 2(2) + 2(4) + 2(6) + 6(-4) = 4+8+12 - 24 = 0 \), which is consistent.
