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. $10\sqrt{2}\,cm$

Answer 1

Answer: (D)

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