Question

Two masses $3\text{kg}$ and $12\text{kg}$ are located at a certain distance and their center of mass is fixed. If the $12\text{kg}$ mass is moved towards the right through a distance of $3\text{m}$, then what is the direction and magnitude of the movement of the $3\text{kg}$ mass?

• A. $12\text{m}$, leftward
• B. $12\text{m}$, rightward
• C. $6\text{m}$, leftward
• D. $6\text{m}$, rightward

Answer 1

The correct option is A $12\text{m}$, leftward

Let the system of masses be as shown below

So, for two mass system we have
$m_1{x}_1=m_2{x}_2$
$\Rightarrow 3x_1=12x_2\Rightarrow x_1=4x_2..\left(i\right)$
Now, the $12\text{kg}$ mass is shifted $3\text{m}$ right, so let us say that $3\text{kg}$ mass is shifted left so that the COM remain unaltered.
So, the condition should be as shown below

Again, we have
$3(x+x_1)=12(x_2+3)$
$\Rightarrow x+x_1=4x_2+12$
From eq $\left(i\right)$, we have
$x=12\text{m}$
Hence, movement of $3\text{kg}$ mass will be $12\text{m}$ leftwards.