Question

Find the centre of mass of a square with side of 2 centimetre having four paricles at its corner of mass 1kg , 2kg , 3kg and 4 kg respectively.

Answer 1

In the fig., let (x, y) be the position of the center of mass.

To find the position of the center of mass, we have the formula,

$\mathbf {r}=\dfrac {\displaystyle\sum_{i=1}^nm_i\mathbf {r_i}}{\displaystyle\sum_{i=1}^nm_i}$

So, about Y axis, the x coordinate of center of mass is,

$x=\dfrac{1(0)+2(2)+3(2)+4(0)}{1+2+3+4}\\\\\\x=\dfrac {10}{10}\\\\\\x=1$

And, about X axis, the y coordinate of the center of mass is,

$y=\dfrac {1(0)+2(0)+3(2)+4(2)}{1+2+3+4}\\\\\\y=\dfrac {14}{10}\\\\\\y=1.4$

Hence the position of the center of mass is,

$\boxed {(x,\ y)=\mathbf {(1,\ 1.4)}}$