A uniform thin rod of mass m and length R is placed normally on the surface of the earth. If the radius of the earth is R and the mass of the earth is M then what is the gravitational force exerted by the earth on the rod?

Hi

Take an elementary stripof length dx at a distance x from surface of earth

So,

dF = GM dm/(R+x)² -------------------(1)

where , dm = m dx/R

putting value of dm in (1)

dF = GM m dx/R(R+x)²

because distance of element from centre of earth = R+x

So,

F = GMm/2R²

integrating wrt x in limit 0 to R

Please approve if u like the answer

Anurag Kishore