Question

Four particles, each of mass 1 kg are placed at the comers of a square OABC of side 1 m. O is at the origin of the co-ordinate system. OA and OC are aligned along positive X-axis and positive V-axis respectively. The position vector of the centre of mass is (in m):

• A. $\widehat{i}-\widehat{j}$
• B. $\frac{1}{2}(\widehat{i}+\widehat{j})$
• C. $(\widehat{i}-\widehat{j})$
• D. $\frac{1}{2}(\widehat{i}-\widehat{j})$

Answer 1

Answer: (B)

$\frac{1}{2}(\widehat{i}+\widehat{j})$

Answer 2

We can show the situation as : The centre of mass of square is at point $D(x,y)$ The position co-ordinate of point D $(x,y)\equiv \left( \frac{0+1}{2},\frac{1+0}{2} \right)$ $=\left( \frac{1}{2},\frac{1}{2} \right)$ Hence, position vector or centre of mass D is $=x\hat{i}+y\hat{j}$ $=\frac{1}{2}\hat{i}+\frac{1}{2}\hat{j}$ $=\frac{1}{2}(\hat{i}+\hat{j})$