Four identical spheres each of mass M and radius 10 cm each are placed on a horizontal surface touching one another so that their centres are located at the corners of a square of side 20 cm . The distance of their centre of mass from the centre of any sphere is

Question

Four identical spheres each of mass M and radius 10 cm each are placed on a horizontal surface touching one another so that their centres are located at the corners of a square of side 20 cm . The distance of their centre of mass from the centre of any sphere is (A) 5 cm (B) 10 cm (C) 20 cm (D) 10√2 cm

Tardigrade Admin · Accepted Answer

As shown in figure, xC M=(M × 0 + M × 20 + M × 20 + M × 0/4 M)=10 cm Similarly yC M=10 cm Hence, distance of centre of mass from centre of any one sphere, Say r=√(10 - 0)2 + (10 - 0)2=10√2 cm

Q. Four identical spheres each of mass $M$ and radius $10 c m$ each are placed on a horizontal surface touching one another so that their centres are located at the corners of a square of side $20 c m$ . The distance of their centre of mass from the centre of any sphere is

$5 c m$

$10 c m$

$20 c m$

$102 c m$

As shown in figure,
$x_{CM} = \frac{M \times 0 + M \times 20 + M \times 20 + M \times 0}{4 M} = 10 c m$
Similarly $y_{CM} = 10 c m$
Hence, distance of centre of mass from centre of any one sphere,
Say $r = (10 - 0)^{2} + (10 - 0)^{2} = 102 c m$

Q. Four identical spheres each of mass M and radius 10cm each are placed on a horizontal surface touching one another so that their centres are located at the corners of a square of side 20cm . The distance of their centre of mass from the centre of any sphere is

5cm

10cm

20cm

102​cm