24Qualitatively we can say that centre of gravity will lie at a relatively lower position
Where is the center of gravity of a very long pole of length L placed vertically on the earths' surface....
(If you think that the answer is obvious.. Think again :P)
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2 Answers
106centre of gravity:
consider an element of length dx situated at height x abv the earths surface.
grav force on it due to earth = GdmM/(R+x)2 (M=mass of earth)
= GλdxM/(R+x)2
Centre of grav is where the point where the earth's grav force can be thought to act on the object.
Total grav force = ∫(0 to l)GλdxM/(R+x)2
= -GλM[1/R+x]0l
= GλM[1/R - 1/(R+L)]
= GλLMR(R+L)
= GmMR(R+L) (m=mass of rod)
Let the centre of grav be situated at h height frm earths surface
So, GmMR(R+L) = GmM/(R+h)2
=> R2+h2+2Rh = R2+RL
=> h2+2Rh - RL = 0
=> h = -R + √R2+RL
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