a body is raised to a height 'nR' from the surface of earth of radius R. show that ratio of acceleration due to gravity on surface to that at given height is (n+1)(n+1)
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We know that mg=GMm/r^2
When body is on surface g=GM/R^2
When body is raised by nR, then g=GM/(R+nR)^2
then g=GM/(R(1+n)^2) taking R common.
now ratio of surface g and new g is
GM/R^2*(R^2)(n+1)^2/GM.
which comes out (n+1)(n+1) or (n+1)^2.
When body is on surface g=GM/R^2
When body is raised by nR, then g=GM/(R+nR)^2
then g=GM/(R(1+n)^2) taking R common.
now ratio of surface g and new g is
GM/R^2*(R^2)(n+1)^2/GM.
which comes out (n+1)(n+1) or (n+1)^2.
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