Question

Three masses are placed on the x-axis: 300 g at origin, 500 g at $x=40$ cm and 400 g at $x=70\text{cm}$. The distance of the centre of mass from the origin

• A. 40 cm
• B. 45 cm
• C. 50 cm
• D. 30 cm

Answer 1

The correct option is A 40 cm

The distance of the centre of mass of the system of three masses from the origin $O$ is
$x_{CM}=\frac{m_1{x}_1+m_2{x}_2+m_3{x}_3}{m_1+m_2+m_3}$
$=\frac{300\times 0+500\times \times 40+400\times 70}{300+500+400}$
$=\frac{500\times 40+400\times 70}{1200}=\frac{400[50+70]}{1200}$
$=\frac{50+70}{3}=\frac{120}{3}=40\text{cm}$
Hence, the correct answer is option (a).