Q. 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. What is the distance of their centre of mass from centre of any sphere?
A) 5 cm
B) 10 cm
C) 20 cm
D) 10$\sqrt{2}$ cm
Explanation
(d) As shown in figure,
$x_{CM} = \frac{M \times 0 + M \times 20 + M \times 20 + M \times 0}{4M} = 10\ cm$
Similarly $y_{CM} = 10\ cm$
Hence, distance of centre of mass from centre of any one sphere,
Say $r = \sqrt{(10 - 0)^{2} + (10 - 0)^{2}} = 10\sqrt{2}\ cm$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.