Question

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

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

Answer 1

The correct option is B ${}^{\frac{1}{2}}(\hat{i}+\hat{j})$

$X_{com}=\frac{\sum \times i}{4}=\frac{1+1+0+0}{4}=\frac{1}{2}$

$Y_{com}=\frac{\sum Y_i}{4}=\frac{0+0+1+1}{4}=\frac{1}{2}$

Position value of $COM=\frac{!}{2}\hat{i}+\frac{1}{2}\hat{i}=\frac{1}{2}(\hat{i}+\hat{j})$.