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 as shown in the figure. If the origin of the coordinate system is taken at the mass of 1 kg, the (x, y) co-ordinates of the centre of mass are

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

Answer 1

The correct option is A

$(1m,\frac{7}{5}m)$

The (x, y) co-ordinates of masses 1 kg, 2 kg, 3 kg and 4 kg respectively are (0, 0), (2 m, 0), (2 m, 2 m), (0, 2 m).
The (x, y) co-ordinates of the centre of mass are given by
$x_{CM}=\frac{1\times 0+2\times 2+3\times 2+4\times 0}{1+2+3+4}=1m{y}_{CM}=\frac{1\times 0+2\times 0+3\times 2+4\times 2}{1+2+3+4}=\frac{7}{5}m$
Hence, the correct choice is (a).