JEE Main & Advanced Mathematics Statistics Centre of Gravity

The centre of gravity of a body or a system of particles rigidly connected together, is that point through which the line of action of the weight of the body always passes in whatever position the body is placed and this point is called centroid. A body can have one and only one centre of gravity.

\[{{w}_{1}},{{w}_{2}},...........,\,{{w}_{n}}\] are the weights of the particles placed at the points \[{{A}_{1}}({{x}_{1}},{{y}_{1}}),{{A}_{2}}({{x}_{2}},{{y}_{2}}),..........,{{A}_{n}}({{x}_{n}},{{y}_{n)}}\] respectively, then the centre of gravity \[G(\bar{x},\bar{y})\] is given by \[\bar{x}=\frac{\sum{{{w}_{1}}{{x}_{1}}}}{\sum{{{w}_{1}}}},\bar{y}=\frac{\sum{{{w}_{1}}{{y}_{1}}}}{\sum{{{w}_{1}}}}\].