Three particles of masses \(50\, g\), \(100\, g\) and \(150\, g\) are placed at the vertices of an equilateral triangle of side \(1\, m\) (as shown in the figure). The \((x, y)\) coordinates of the centre of mass will be

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Correct Answer

(D) \(\left( {\frac{7}{{12}}m,\,\frac{{\sqrt 3 }}{4}\,m} \right)\)

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Detailed explanation

The co-ordinates of the center of mass

\({\overrightarrow r _{cm}} = \frac{{0 + 150 \times \left( {\frac{1}{2}i + \frac{{\sqrt 3 }}{2}\hat j} \right) + 100 \times \hat i}}{{300}}\)

\({\overrightarrow r _{cm}} = \frac{7}{{12}}\hat i + \frac{{\sqrt 3 }}{4}\hat j\)

\(\therefore \,\,Co - ordinate\left( {\frac{7}{{12}},\frac{{\sqrt 3 }}{4}} \right)m\)

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