Question

three masses 5kg 8kg and 6 kg are kept at the vertices of an equilateral triangle of side length 2m find the centre of mass of the system of masses considering 5 kg at origin.​

Answer 1

Given:-

Three masses 5 kg, 8 kg and 6 kg at the vertices of equilateral triangle of side 2 m.

To Find:-

center of mass

Explanation:-

$\text{The general expression to calculate co-ordinates of center of mass is given by:-}\\\\\bar{x}=\dfrac{m_{1}x_{1}+m_{2}x_{2}+m_{3}x_{3}}{m_{1}+m_{2}+m_{3}}\text{ and }\bar{y}=\dfrac{m_{1}y_{1}+m_{2}y_{2}+m_{3}y_{3}}{m_{1}+m_{2}+m_{3}}\\\\\Rightarrow\bar{x}=\dfrac{(5\times0)+(8\times1)+(6\times2)}{5+8+6}=1.053m\\\\\Rightarrow\bar{y}=\dfrac{(5\times0)+(8\times\sqrt{3})+(6\times0)}{5+8+6}=0.73m\\\\\text{Therefore, co-ordinates of center of mass is (1.053,0.73)}.$