Question

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

Options

• 375 N

• 125 N

• 500 N

• 72.5 N

Answer 1

125 N

Explanation:

When weighted on the surface weight w = mg = 250 N

∴ mass m = `"w"/"g" = 250/10` = 25 kg

Acceleration due to gravity g varies with depth as

`"g"^1 = "g"^1 = "g" (1 - "d"/"R") = "g"(1 - "R"/2_"R")` [∴ d = R/2 given]

∴ g¹ = g/2

∴ weight, half way down to the center of earth

w = mg¹ = `25 xx "g"/2 = 25 xx 10/2` = 125 N