Question

Three small spheres A , B and C of masses $50g.100g$ and $150g$ are placed at the vertices of an equilateral triangle of side $1m$ (as shown in the figure). The $\left(\right.x,y\left.\right)$ coordinates of the centre of mass will be:

• A. $\left(\frac{7}{12} m \frac{\sqrt{3}}{4} m\right)$
• B. $\left(\frac{7}{12} m , \frac{\sqrt{3}}{8} m\right)$
• C. $\left(\frac{\sqrt{3}}{4} m , \frac{5}{12} m\right)$
• D. $\left(\frac{\sqrt{3}}{8} m \frac{7}{12} m\right)$

Answer 1

Answer: (A)

$x_{cm}=\frac{50 \times 0 + 100 \times 1 + 150 \times 1 / 2}{50 + 100 + 150}$
$=\frac{175}{300}=\frac{7}{12}cm$
$y_{cm}=\frac{50 \times 0 + 100 \times 0 + 150 \sqrt{3} / 2}{300}=\frac{\sqrt{3}}{4}cm$