Question

Masses of $2 \,kg$ each are placed at the corners $B$ and $A$ of a rectangular plate $A B C D$ as shown in the figure. A mass of $8 \,kg$ has to be placed on the plate so that the centre of mass of the system should be the centre O. Then the mass should be placed at:

• A. 1m from O on OE
• B. 2m from O on OF
• C. 2m from O on OG
• D. 2m from O on OH

Answer 1

Answer: (A)

$x_{ cm }=\frac{m_{1} x_{1}+m_{2} x_{2}+m_{3} x_{3}}{m_{1}+m_{2}+m_{3}}$
$\Rightarrow 0=\frac{2(-2)+2(-2)+8 x_{3}}{2+2+8} $
$\Rightarrow x_{3}=1 m$