Question

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

• A. $42.5\text{cm}$
• B. $45\text{cm}$
• C. $60\text{cm}$
• D. $30\text{cm}$

Answer 1

The correct option is A $42.5\text{cm}$


The masses $m_1=300\text{gm}$, $m_2=400\text{gm}$, $m_3=500\text{gm}$ are placed at $x_1=0,x_2=40\text{cm},x_3=70\text{cm}$ respectively as shown in the above figure.

Applying the formula for $x$ coordinate of COM of system:

$x_{\text{COM}}=\frac{m_1{x}_1+m_2{x}_2+m_3{x}_3}{m_1+m_2+m_3}$

$=\frac{(300\times 0)+(400\times 40)+(500\times 70)}{300+500+400}$

$=\frac{16000+35000}{1200}=\frac{170}{4}=42.5\text{cm}$