Three bodies each of mass $1 \mathrm{~kg}$ are situated at the vertices of an equilateral triangle of side…

Three bodies each of mass $1 \mathrm{~kg}$ are situated at the vertices of an equilateral triangle of side $1 \mathrm{~m}$. The $x y$-coordinates of centre of mass of the system are.
  1. $\left(\frac{1}{2 \sqrt{3}}, \frac{1}{2 \sqrt{3}}\right)$
  2. $\left(\frac{1}{2 \sqrt{3}}, \frac{1}{2}\right)$
  3. $\left(\frac{1}{2}, \frac{1}{2}\right)$
  4. $\left(\frac{1}{2}, \frac{1}{2 \sqrt{3}}\right)$

Solution

$\begin{aligned} & X_{\mathrm{cm}}=\frac{0+(1 \times 1)+(1 \times 0.5)}{3}=\frac{1}{2} \mathrm{~m} \\ & Y_{\mathrm{cm}}=\frac{0+0+\left(1 \times \frac{\sqrt{3}}{2}\right)}{3}=\frac{1}{2 \sqrt{3}} \mathrm{~m}\end{aligned}$

Asked in: MHT CET 2022 (11 Aug Shift 1)

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