Question

A mass m is at a distance a from one end of a uniform rod of length l and mass M. Find the gravitational force on the mass due to the rod.
A. `(GM^(2))/(L^(2))`
B. `(GM^(2))/(2L^(2))`
C. `(2GM^(2))/(3L^(2))`
D. `(4GM^(2))/(9L^(2))`

Answer 1

Correct Answer - B
Consider an element of the rod of length `dx` at adistance `x` from point mass as shown in Fig.

Mass of element `= (M//L)dx`
Force experienced by point mass due to this
element is `dF = (GM xx (M//L) dx)/(x^(2)) = (GM^(2))/(L) (dx)/(x^(2))`
Total force experienced by point mass due to whole
rod is `F = int_(L)^(2L) (GM^(2))/(L) (dx)/(r^(2)) = (GM^(2))/(2L^(2))`