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Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
हिन्दीThree particles of masses \( 100\text{ g} \), \( 150\text{ g} \), and \( 200\text{ g} \) are placed at the vertices of an equilateral triangle of side \( 0.5\text{ m} \) as shown in the text coordinate system: \( 100\text{ g} \) at \( (0,0) \), \( 150\text{ g} \) at \( (0.5,0) \), and \( 200\text{ g} \) at \( (0.25, 0.25\sqrt{3}) \). What is the distance of the centre of mass from the origin?
Correct answer · Option 3
\( \frac{\sqrt{37}}{18}\text{ m} \)
Explanation
\( X = 5/18\text{ m} \), \( Y = 1/(3\sqrt{3}) = \sqrt{3}/9 = 2\sqrt{3}/18\text{ m} \). \( R = \sqrt{X^2 + Y^2} = \frac{\sqrt{5^2 + (2\sqrt{3})^2}}{18} = \frac{\sqrt{25 + 12}}{18} = \frac{\sqrt{37}}{18}\text{ m} \).
