question_answer

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)  \[\frac{1}{2}(\widehat{i}-\widehat{j})\]

Correct Answer: B

Solution :

                 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 \[=x\hat{i}+y\hat{j}\] \[=\frac{1}{2}\hat{i}+\frac{1}{2}\hat{j}\] \[=\frac{1}{2}(\hat{i}+\hat{j})\]