Question

Two particles of mass $1kg$ and $2kg$ are kept on a horizontal plane as shown in the figure. The distance between them is $5m$.Mass of $1kg$ shifted to point A and that of $2kg$ shifted to the point B such that center of mass of mass of the system does not change then distance the masses will:

• A. increases
• B. does not change
• C. $\frac{\sqrt{37}}{2}$
• D. $\frac{\sqrt{73}}{2}$

Answer 1

The correct option is A increases

$x_{cm}=\frac{2\times 3}{2+1}=2cm$
$y_{cm}=\frac{2\times 4}{2+1}=\frac{8}{3}cm$
find $x_{cm}$ and you are same as initial
$B=(x,0)$ $A=(o,y)$
$x_{cm}=\frac{2\times x}{2+1}=2$
$x=3cm$
$y_{cm}=\frac{1\times y}{2+1}=\frac{8}{3}=y=8cm$
new
Distance $AB=\sqrt{3^2+8^2}=\sqrt{73}$
Which is more than $5$ so distance has increased