Question

Masses of $1$kg each are placed $1$m, $2$m, $4$m, $8$m,... from a point P. The gravitational field intensity at P due to these masses is?

• A. $G/2$
• B. G
• C. $4$G
• D. $4G/3$

Answer 1

Answer: (D)

$4G/3$

$F=\sum \frac{G{m}_1{m}_2}{r^2}$

$=$ $\frac{G\times 1\times 1}{1^2}+\frac{G\times 1\times 1}{2^2}+\frac{G\times 1\times 1}{4^2}+\frac{G\times 1\times 1}{8^2}+......$

$=G[\frac{1}{1}+\frac{1}{2^2}+\frac{1}{4^2}+\frac{1}{8^2}]$

$=G[1+\frac{1}{4}+\frac{1}{16}+\frac{1}{64}]$

$=G\left[\frac{1}{1-\frac{1}{4}}\right]$

$=G\times \frac{1}{\frac{3}{4}}$

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