Question

Mass particles of 1 kg each are placed along x-axis at x = 1, 2, 4, 8,.....$\infty$ then gravitational field intensity at origin is (G = universal gravitational constant):

• A. $\frac{4G}{3}$
• B. $\frac{2G}{4}$
• C. 26
• D. $\infty$

Answer 1

The correct option is A $\frac{4G}{3}$

Gravitational field, $E=\frac{GM}{r^2}$

Thus gravitational field intensity at origin due to all the particles $E=\frac{GM}{1^2}+\frac{GM}{2^2}+\frac{GM}{4^2}+\frac{GM}{8^2}+...........upto\infty terms$

$E=GM[\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{4^2}+\frac{1}{8^2}+...........upto\infty terms]$

$E=GM[\frac{1}{1-\frac{1}{4}}]$ where $M=1kg$

$E=\frac{4G}{3}$