Physics - Center of Mass Question with Solution | TestHub
A system consists of three particles, each of mass and located at (1,1),(2,2) and (3,3) . The co-ordinates of the centre of mass are
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Solution:
The coordinates of C.M of three particle are \begin{array}{c} \mathrm{x}=\frac{\mathrm{m}_{1} \mathrm{x}_{1}+\mathrm{m}_{2} \mathrm{x}_{2}+\mathrm{m}_{3} \mathrm{x}_{3}}{\mathrm{~m}_{1}+\mathrm{m}_{2}+\mathrm{m}_{3}} \& \mathrm{y}=\frac{\mathrm{m}_{1} \mathrm{y}_{1}+\mathrm{m}_{2} \mathrm{y}_{2}+\mathrm{m}_{3} \mathrm{y}_{3}}{\mathrm{~m}_{1}+\mathrm{m}_{2}+\mathrm{m}_{3}} \\ \text { here } \mathrm{m}_{1}=\mathrm{m}_{2}=\mathrm{m}_{3}=\mathrm{m} \\ \text { so } \mathrm{x}=\frac{\left(\mathrm{x}_{1}+\mathrm{x}_{2}+\mathrm{x}_{3}\right) \mathrm{m}}{\mathrm{m}+\mathrm{m}+\mathrm{m}}=2 \end{array} so coordinates of . of three particle are (2,2)