Assuming the earth to be a sphere of uniform mass density, how much would a body weigh half way down to the centre of the earth if it weighed 250 N on the surface ?

Assuming the earth to be a sphere of uniform mass density, how much wo

1.	Assuming the earth to be a sphere of uniform mass density, how much would a body weigh half way down to the centre of the earth if it weighed 250 N on the surface ?
Answer» Solution :`IMPLIES` Suppose, G and `g_d`are the acceleration DUE to gravity at the surface and at the depth d of earth respectively and `W and W_d` are the weights of body at the surface and at the depth of earth respectively. `g(d) = g(1-d/R)` `:. g(d) = g (1-(R/2)/R)""[ :. d = R/2]` `= g (1-1/2)` `=g/2` `:.`Weight of body of mass m at depth d W(d) = mg (d) `=(mg)/2 ""[ :. g(d) =g/2]` `W(d) = W/2 ""[ :. mg = W]` `:. W(d) = (250)/2` `:. W(d) = 125 N`