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Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
हिन्दीThree particles of masses \( 1 \text{ kg} \), \( 2 \text{ kg} \), and \( 3 \text{ kg} \) are located at the vertices of an equilateral triangle of side length \( 2 \text{ m} \) in the \( xy \)-plane with \( 1 \text{ kg} \) at \( (0, 0) \) and \( 2 \text{ kg} \) at \( (2, 0) \). The distance of the centre of mass from the \( 1 \text{ kg} \) particle is:
Correct answer · Option 3
\( \frac{\sqrt{19}}{3} \text{ m} \)
Explanation
Coordinates: \( (0,0) \), \( (2,0) \), and \( (1, \sqrt{3}) \). \( X_{\text{cm}} = \frac{1(0)+2(2)+3(1)}{6} = \frac{7}{6} \), \( Y_{\text{cm}} = \frac{1(0)+2(0)+3(\sqrt{3})}{6} = \frac{\sqrt{3}}{2} \). Distance \( d = \sqrt{(\frac{7}{6})^2 + (\frac{\sqrt{3}}{2})^2} = \sqrt{\frac{49}{36} + \frac{27}{36}} = \frac{\sqrt{76}}{6} = \frac{2\sqrt{19}}{6} = \frac{\sqrt{19}}{3} \text{ m} \).
