Question

3. Show that, if variations of gravity are taken into account, the time in which a particle falls to the Earth's surface from a height h is 1/2 2h 1 5h approximately, h being much smaller than the Earth's radius a

Answer 1

Effect of Altitude consider earth to be a sphere of mass m, radius � a � with center at O . Let � g � be value of acceleration due to gravity at a point A on the surface of Earth . Therefore g = G M/a^2 If g � is the acceleration due to gravity at a point B, at a height � h � above the surface of earth, then the force an the body at B is due to earth where mass � M � is concentrated at the center � O � of earth . g � = G M/(R + h)^2 Dividing (ii) by (i) , we get g �/g = G M/(a + h)^2 times a^2/G M = (a/a + h)^2 \r\n Take � a^2 � common
There is one mistake in your question i.e. 5/6 in the second bracket. It should be only '1'.Because my method is completly perfect.I have checked many books and google for it.I am pretty sure about the solution of this question.