question_answer

Four particles of mass 2 kg, 3 kg, 4 kg and 8 k) are situated at the corners of a square of side length 2m, the centre of mass may be given as

A) \[\left( \frac{30}{18},\frac{28}{18} \right)\]                         

B) \[\left( \frac{20\sqrt{2}}{18},\frac{24\sqrt{2}}{18} \right)\]

C) \[\left( \frac{14}{17},\frac{24}{17} \right)\]                         

D) \[\left( \frac{34}{18},\frac{34}{18} \right)\]         

Correct Answer: C

Solution :

Consider the situation In this situation, coordinates of centre of mass coordinate,\[x=\frac{2\times 0+3\times 2+4\times 2+8\times 0}{2+3+4+8}=\frac{14}{17}\] y - coordinate,\[y=\frac{2\times 0+8\times 2+2\times 4+2+3\times 0}{2+3+4+8}\] \[=\frac{24}{17}\] Thus, coordinate is\[\left( \frac{24}{17},\frac{24}{17} \right)\]