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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
F = GMm/2R2
integrating wrt x in limit 0 to R
Please approve if u like the answer
Anurag Kishore
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