Question

A small mass and a thin uniformed rod each of mass 'm' are positioned along the same straight line as shown. find the forced of gravitational attraction exerted by the rod on the small mass.

Answer 1

The segment of the rod of length dx has a man 'm',The mass per units length is constant

$\therefore$ force of gravitational attraction exerted by rod on the small man dm is

$F=-Gm{\int }_L^{3L}\frac{dm}{x^2}=F=\frac{-G{m}^2}{2L}{\int }_L^{3L}\frac{dx}{x^2}$

$=F=\frac{-G{m}^2}{2L}(-\frac{1}{x})\Rightarrow \therefore F=\frac{G{m}^2}{3L^2}$

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