Question

find the centre of gravity of a uniform square plate ABCD of weight 10lbs together with weight 20, 30, 40, 50lbs placed at it corner A,B,C,D respectively

​

Answer 1

∵ initial center of mass stays at the center of the square plate. When the mass (20 g) are placed at B and C, the shift along 'y' direction is Zero.

It moves towards the line

OY

Answer 2

Answer:

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.

\begin{gathered}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}\end{gathered}

x=

m

1

+m

2

+m

3

m

1

x

1

+m

2

x

2

+m

3

x

3

y=

m

1

+m

2

+m

3

m

1

y

1

+m

2

y

2

+m

3

y

3

here, m_1=1kg,m_2=m_3=0.02kgm

1

=1kg,m

2

=m

3

=0.02kg

x_1=0,x_2=L,x_3=Lx

1

=0,x

2

=L,x

3

=L

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

1+0.02+0.02

0+0.02L+0.02L

x = 0.04L/1.04 = 4L/104

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

1

=0,y

2

=L,y

3

=−L

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

1+0.02+0.02

0+0.02L−0.02L

y = 0

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

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