Question

Infinite number of particles each of mass ${}^{\prime }{m}^{\prime }$ are at points $(l,0),(2l,0),(4l,0),(8l,0)$ etc. Then the intensity of gravitational field at the origin is:-

• A. $\frac{3Gm}{2l^2}$
• B. Infinity
• C. $\frac{4Gm}{3l^2}$
• D. $\frac{3Gm}{4l^2}$

Answer 1

The correct option is C $\frac{4Gm}{3l^2}$

The magnitude of gravitational field intensity at point $O$ will be sum of gravitational field intensity due to each mass $m$

$I=Gm[\frac{1}{l^2}+\frac{1}{{\left(2l\right)}^2}+\frac{1}{{4l}^2}-]$

$=\frac{Gm}{r^2}[1+\frac{1}{2^2}+\frac{1}{4^2}+\frac{1}{8^2}-]$

$=\frac{Gm}{r^2}\left[\frac{1}{1-\frac{1}{2^2}}\right]$

$=\frac{Gm}{r^2}\left[\frac{1}{1-\frac{1}{4}}\right]$

$=\frac{4Gm}{3l^2}$