Question

A uniform square plate abcd has a mass of 1kg. if two point masses each of 20g are placed at b and c then centre of mass shifts on?

Answer 1

Centre of mass shifts on = OY

Answer 2

we know, centre of mass of uniform square plate lies on geometrical centre. in figure , it is given that initial centre of mass of square plate is located at origin.
assume side length of square plate is 2L, then,
a(-L,L) , b(L,L), c(L,-L) and d(-L,-L)

now two point masses each of mass 20g or 0.02kg are placed at b and c corner of square plate.

use basic concept of centre of mass.

$x=\frac{m_1x_1+m_2x_2+m_3x_3}{m_1+m_2+m_3}\\\\y=\frac{m_1y_1+m_2y_2+m_3y_3}{m_1+m_2+m_3}$

here, $m_1=1kg,m_2=m_3=0.02kg$
$x_1=0,x_2=L,x_3=L$

so, $x=\frac{0+0.02L+0.02L}{1+0.02+0.02}$

x = 0.04L/1.04 = 4L/104

similarly, $y_1=0,y_2=L,y_3=-L$

$y=\frac{0+0.02L-0.02L}{1+0.02+0.02}$

y = 0

hence, new centre of mass is (4L/104 , 0)

here it is clear that centre of mass is shifted along OY.