Three particles each of mass $m$ are placed at the corners of an equilateral triangle of side a as shown in the figure. The $x$ -co-ordinate of centre of mass will be

\frac{\sqrt{3} a}{2}

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\frac{3 a}{4}

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\frac{a}{2}

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Solution

The correct option is C $\frac{a}{2}$
X coordinate of COM is given by
$X_{c m} = \frac{m_{1} x_{1} + m_{2} x_{2} + m_{3} x_{3}}{m_{1} + m_{2} + m_{3}}$
$\Rightarrow X_{c m} = \frac{m \times 0 + m \times a + m \times \frac{a}{2}}{3 m}$
$\Rightarrow X_{c m} = \frac{a}{2}$

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The correct option is C $\frac{a}{2}$
X coordinate of COM is given by
$X_{c m} = \frac{m_{1} x_{1} + m_{2} x_{2} + m_{3} x_{3}}{m_{1} + m_{2} + m_{3}}$
$\Rightarrow X_{c m} = \frac{m \times 0 + m \times a + m \times \frac{a}{2}}{3 m}$
$\Rightarrow X_{c m} = \frac{a}{2}$