Question

Four particles, each of mass $1kg$, are placed at the corners of a square of side one meter in the $X-Y$ plane. If the point of intersection of the diagonals of the square is taken as the origin, the coordinates of the centre of mass are :

• A. $(1,1)$
• B. $(-1,1)$
• C. $(1,-1)$
• D. $(0,0)$

Answer 1

Answer: (D)

$(0,0)$

$x_{com}=\frac{\sum m_i{x}_i}{\sum m_i}$

$=\frac{1\times \frac{1}{2}+1\times (-\frac{1}{2})+1\times (-\frac{1}{2})+1\times \left(\frac{1}{2}\right)}{4}$

$x_{com}=0$

Similarly $y_{cm}=\frac{\sum m_i{y}_i}{\sum yi}$

$y_{cm}=\frac{1\times \frac{1}{2}+1\times \frac{1}{2}+1\times (-\frac{1}{2})+1\times (-\frac{1}{2})}{4}$

$y_{cm}=0$

Hence coordinate of com

$(x_{cm},y_{cm})=(0,0)$

Option D.