Question

Infinite number of masses, each $ 1 \,kg $ , are placed along the $ x-axis $ at $ x=\pm \text{ }1\text{ }m,\pm 2m,\pm \text{ }4 $ $ m,\pm \text{ }8\text{ }m,\pm \text{ }16m.... $ The magnitude of the resultant gravitational potential in terms of gravitational constant $ G $ at the origin $ (x=0) $ is

• A. $ G/2 $
• B. $ G $
• C. $ 2G $
• D. $ 4G $

Answer 1

The Correct Option is C

Gravitational potential
$ V=GM\left( \frac{1}{{{r}_{1}}}+\frac{1}{{{r}_{2}}}+\frac{1}{{{r}_{3}}}+...... \right) $
$ =G\times 1\left( \frac{1}{1}+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+.... \right) $
$ =G\left( \frac{1}{1-1/2} \right) $
$ \left( \because sum\,of\,GP=\frac{a}{1-r} \right) $