Question

Distance from one end of a uniform rod of length l and mass m find the gravitational force on the mass due to the rod

Answer 1

◆【Solution】◆

This type of question is my favourite as I need to do integration so let's start....

Mass per unit length of rod = M/L

Mass of rod = M

Length of rod = L

Mass of point = m

Distance between end of rod and point mass = R

I take a element on rod at a distance of x from the point mass of width dx.

Mass of the element = M.dx/L

Force of Attraction = GM.(M.dx/L)/x²

dF = GM².dx/Lx²

dF = (GM²/L)(dx/x²)

∫dF = (GM²/L) ∫dx/x²

Limit of force goes from 0 to F

Limit of X goes from R to R + L

(F - 0) = (GM²/L)(-1/X)

F = (GM²/L)[-1/(R+L) + 1/R]

◆【F = (GM²/L)[1/R - 1/(R+L)]】◆

#answerwithquality

#BAL