AP EAMCET Engineering 21 Apr 2019 Shift 1 Paper

The expression for the centre of the mass of the spheres is,
xCM=‌

m1x1+m2x2+m3x3

m1+m2+m3

The centre of the mass of the spheres along the x axis is calculated as,
xCM‌‌=‌

m

3m

(0+2√3+√3)
‌‌=‌

3√3

3

‌‌=√3
The centre of the mass of the spheres along the y axis is calculated as,
yCM‌‌=‌

m

3m

(0+0+3)
‌‌=1
The coordinates of the centre of the mass of the sphere is
CCM=(√3,1)
According to the given condition, the centre of sphere when one sphere is removed is,
xCM′‌‌=‌

0+2√3

2

‌‌=√3
The below diagram is a representation of spheres after the exclusion of one sphere.

The new coordinates of the centre of mass of the spheres is CCM′=(√3,0), which implies that the centre of the mass is shifted by 1m in y direction.