Question

A large number of identical point masses $m$ are placed along $x-axis,$ at $x=0,1,2,4,.....$ The magnitude if gravitational force on mass at origin ($x=0,$) will be

• A. $G{m}^2$
• B. $\frac{4}{3}G{m}^2$
• C. $\frac{2}{3}G{m}^2$
• D. $\frac{5}{4}G{m}^2$

Answer 1

The correct option is D $\frac{5}{4}G{m}^2$

$\begin{array}{c}{F}_g=\frac{GMm}{r^2}\\ F_g=GMm\left(\frac{1}{12},\frac{1}{22},\frac{1}{42}.......\right)\left(thus,GP\right)\\ SumofG.P=\frac{a}{1+r}=\frac{1}{1+\frac{1}{4}}=\frac{4}{5}\\ Hence,\\ F_{net}=\frac{G{m}^2}{\frac{4}{5}}=\frac{5}{4}G{m}^2\\ \therefore optionDiscorrectanswer.\end{array}$