Q. Infinite number of bodies, each of mass 2 kg, are situated on x-axis at distances 1 m, 2 m, 4 m, 8 m, … respectively, from the origin. The resulting gravitational potential due to this system at the origin will be
A) −G
B) −(8/3)G
C) −(4/3)G
D) −4G
Explanation
[Solution from source] V = −Gm(1/1 + 1/2 + 1/4 + 1/8 + …) = −G × 2 × [1/(1 − 1/2)] = −G × 2 × 2 = −4G. Forgetting the 2 kg mass gives −2G-type answers; the sum of the geometric series is 2. Answer (4).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.