Question

Four particles, each of mass 'm', are placed at the corners of a square of side 'a' shown in the figure. The position vector of the centre of mass is

• A. $a(i+j)$
• B. $\frac{a}{2}(i+j)$
• C. $a(i-j)$
• D. $\frac{a}{2}(i-j)$

Answer 1

The correct option is B $\frac{a}{2}(i+j)$



The (x, y) co-ordinates of the masses at O, A, B and C respectively are
$(x_1=0,y_1=0),(x_2=a,y_2=0),(x_3=a,y_3=a),(x_4=0,y_4=a).$
Therefore, the (x,y) co-ordinates of the centre of mass are
$x_{CM}=\frac{a}{2}and{y}_{CM}=\frac{a}{2}$. The position vector of the centre of mass is
$\frac{a}{2}(i+j)$, which is choice (b)