Question

Four Particles of masses 1 kg, 2 kg, 3 kg, and 4 kg are placed at the corners of a square of side 2 m in the x – y plane in anticlockwise sense. If the origin of the co-ordinate system is taken at the mass of 1 kg, the (x, y) co-ordinates of the centre of mass, expressed in 'metre' are

• A. $(3,\frac{7}{5})$
  
• B. $(2,\frac{7}{5})$
  
• C. $(1,\frac{7}{5})$
  
• D. $(4,\frac{7}{5})$

Answer 1

The correct option is C $(1,\frac{7}{5})$


The (x, y) co - ordinates of masses 1 kg, 2kg, 3kg and 4kg respectively are
$(x_1=0,y_1=0),(x_2=2m,y_2=0),(x_3=2m,y_3=2m),(x_4=0,y_4=2m).$
The (x, y) co-ordinates of the centre of mass are
$x_{CM}=\frac{1kg\times 0+2kg\times 2m+3kg\times 2m+4kg\times 0}{1kg+2kg+3kg+4kg}=1m$
$y_{CM}=\frac{1kg\times 0+2kg\times 0+3kg\times 2m+4kg\times 2m}{1kg+2kg+3kg+4kg}=\frac{7}{5}m$