Question

The position of centre of mass of a system consisting of two particles of masses $m_1$ and $m_2$ separated by a distance $L$ apart, from $m_1$ will be

• A. $\frac{m_{1}L}{m_1+m_2}$
• B. $\frac{m_{2}L}{m_1+m_2}$
• C. $\frac{m_2}{m_1}L$
• D. $\frac{L}{2}$

Answer 1

The correct option is B $\frac{m_{2}L}{m_1+m_2}$

Taking the the mass $m_1$ at $origin$ we may write its position as $x_1=0$

and position of $m_2$ at $x=0+L=L$

now position of center of mass will be $X_{cm}=\frac{m_1{x}_1+m_2{x}_2}{m_1+m_2}=\frac{0+m_{2}L}{m_1+m_2}$

or $X_{cm}=\frac{m_2}{m_1+m_2}L$