Question

Three identical spheres of mass $M$ each are placed at the corners of an equilateral triangle of side $2m$ . Taking one of the corners as the origin as shown in the figure, the position vector of the centre of mass is

• A. $\sqrt{3}$ ( $\hat{\text{i}}$ - $\hat{\text{j}}$ )
• B. $\frac{\hat{i}}{\sqrt{3}}+\hat{j}$
• C. $\frac{\hat{\text{i}}\text{+}\hat{\text{j}}}{3}$
• D. $\hat{i}+\frac{\hat{j}}{\sqrt{3}}$

Answer 1

Answer: (D)

The $x$ coordinate of centre of mass is


$x_{com}=\frac{\sum M_i{x}_i}{\sum M_i}$
$=$ $\frac{M\times 0+M\times 1+M\times 2}{M+M+M}$ $=1$
$y_{com}=\frac{\sum m_i{y}_i}{\sum m_i}$
$=$ $\frac{M\times 0+M\times (2sin60)+M\times 0}{M+M+M}$
$y_{com}=\frac{\sqrt{3}M}{3M}=\frac{1}{\sqrt{3}}$
Position vector of centre of mass is $\left(\hat{i}+\frac{\hat{j}}{\sqrt{3}}\right)$ .