Question

Masses of $2kg$ each are placed at the corners $B$ and $A$ of a rectangular plate $ABCD$ as shown in the figure. A mass of $8kg$ to be placed on the plate so that the center of mass of the system should be at the $centerO.$ Then the mass should be placed at:

• A. $1mfromOonOE$
• B. $2mfromOonOF$
• C. $2mfromOonOG$
• D. $2mfromOonOH$

Answer 1

The correct option is A $1mfromOonOE$

Let the origin be @ Q.

x let the 8 kg mass be placed @ P

Coordinates : $Q=(0,0)$

$A=(-2,-l/2)$

$B=(-2,+l/2)$

$P=(x,y)$ say.

$Y_{cm}=\frac{2\times -\frac{l}{2}+2\times +\frac{l}{2}+8xy}{M}=0$ (given)

$\Rightarrow 0+8y=0\Rightarrow y=0$

$X_{cm}=\frac{2\times -2+2\times -2+x\times 8}{M}=0$

$\Rightarrow -8+8x=0$

$\Rightarrow x=1m$

$\therefore$ Point P is on OE 1 m from Q.

Ans : A