Two iron spheres are in contact The outside diameter of both

Two iron spheres are in contact. The outside diameter of both spheres is 100 mm. At what distance \"r\" from the center of the earth, will the force of of mutual attraction between the contacting spheres be equal to the force exerted by the earth on one of the spheres. The answer should be r = 1.258 x 10⁸ km

Solution

Here ,

let the distance from the earth is d

Radius of earth , R = 1.258 *10^8 km

R = 1.258 *10^11 m

Now , for the mutual force to be equal

G * (m) * M/(1.258 *10^11 + d)^2 = G * m^2/0.2^2

5.98 *10^24/(1.258 *10^11 + d)^2 = 4/3 pi * 0.10^3 * 7870/0.2^2

solving for d

d = -0.40 *10^11 m , distance = 1.258 *10^11 - 0.40 *10^11 = 0.858 *10^11 m

the distance from the centre of earth is 0.858 *10^11 m