Find the gravitational attraction between to solid spheres e

Find the gravitational attraction between to solid spheres each with mass of I kg and density of 11.35 g/cm^3 Consider that the spheres are almost in contact. Give your answer as a fraction of the weight of either of sphere.

Solution

Mass = 1 kg

density = 11.35 gm/cm^3 = 11350 kg/m^3

mass = density*volume

volume = 1/11350 = 8.81*10^-5 m^3

V = (4/3)*pi*r^3

r = (8.81*10^-5*3/(4*3.14))^(1/3) = 0.0276 m

F = Gm1*m2/d^2

d = r1 + r2 = 2*r1 = 0.0552 m

F = 6.67*10^-11*1*1/(0.0552)^2 = 2.19*10^-8 N

W = Weight of sphere = mg = 1*9.81 = 9.81 N

Answer F/W = 2.19*10^-8/9.81 = 2.23*10^-9

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