Question

Three point particles of mass 1 kg, 1.5 kg and 2.5 kg are placed at three corners of a right triangle of sides 4.0 cm, 3.0 cm and 5.0 cm as shown in the figure. The centre of mass of the system is at the point:

• A. 0.9 cm right and 2.0 cm above 1 kg mass
• B. 2.0 cm right and 0.9 cm above 1 kg mass
• C. 1.5 cm right and 1.2 cm above 1 kg mass
• D. 0.6 cm right and 2.0 cm above 1 kg mass

Answer 1

The correct option is A 0.9 cm right and 2.0 cm above 1 kg mass

Taking 1 kg as the origin
$$\begin{array}{cc}& x_{com}=\frac{m_1{x}_1+m_2{x}_2+m_3{x}_3}{m_1+m_2+m_3}\\ & x_{com}=\frac{1\times 0+1.5\times 3+2.5\times 0}{5}\\ & x_{com}=0.9\\ & y_{com}=\frac{m_1{y}_1+m_2{y}_2+m_3{y}_3}{m_1+m_2+m_3}\\ & y_{com}=\frac{1\times 0+1.5\times 0+2.5\times 4}{5}\\ & y_{com}=2\end{array}$$
Centre of mass is at $(0.9,2)$