A body weighs 63 N on the surface of the earth. What is the gravitational force on it due to the earth at a height equal to half the radius of the earth ?

Explanation

`implies` Here `h = (R_E)/ 2`
Acceleration due to gravity at height h from the surface of earth,
`g(h) = g_e/((1+h/R_E)^2)`
`= (g_e)/([1+(R_E/2)/(R_E)]^(-2))[:. h=R_E/2]`
`=g_e/((1+1/2)^2)`
`:. g(h) = 4/9 "ge"`
Weight on earth W = mg = 63 N
Weight at a height equal to half of radius of the earth `(h =(R_E)/2)` from the surface of earth.
`W= mg (h) = 4/9 "mge"`
`:. W. = 4/9 (63) [ :. mg_e = 63 N]`
`:. W. = 28 N`