Question

A coordinate axis system taking x-axis as horizontal smooth floor is shown in figure. Two small balls of masses $m$ and $3m$ attached with a string are released from some heights on y-axis as shown in figure. The balls may collide head on or obliquely. After a certain time mass $m$ is at $(9cm,20cm)$ while mass $3m$ is $25cm$ above the x axis and the strings is taut. The balls always remain in x-y plane. Find the length of string.

Answer 1

Mass $3$ lie along line $AB$ whose $y$ coordinate is $25cm$

We know that the $x$ - coordinate of center of mass of both bll is at zero

then

$x_{com.}\frac{3mx+9m}{3m+m}=0x=-\frac{9}{3}=-3cm$

So coordinate of $3m$ mass is $(-3,25)$cm

Length of string will be

$=\sqrt{{(9+3)}^2+{(25-20)}^2}=\sqrt{{\left(12\right)}^2+{\left(5\right)}^2}=\sqrt{144+25}=\sqrt{169}=13cm$