Question

The distance between the earth and moon is 3.85×10² m. at what point gravitational field intensity be zero? Mass of earth=6.0×10²⁴ kg, mass of moon 7.26×10²² kg​

Answer 1

The gravitational field intensity will be zero at a distance of 3.46 x 10⁸ m from earth

We know that the gravitational field intensity is given by,

E = GM/r²

The gravitational field intensity will be zero at a point where both the intensity will be equal and opposite. Let it will be at x meter from the earth, then it will be (D-x) mtrs from moon.

where D = distance between earth and moon = 3.85 x 10⁸ m

Hence,

G x 6 x 10²⁴/x² = G x 7.26 x 10²²/(D-x)²

=>7.26 x² = 600(D-x)²

=> x² = 82.64(D-x)²

=> x = 9.09(D-x)

=> x = 9.09D - 9.09x

=> 10.09x = 9.09D

=> x = 9.09D/10.09 = 0.9D

putting the value of D = 3.85 x 10⁸, we get

x = 0.9 x 3.85 x 10⁸ = 3.46 x 10⁸ m

Hence at a distance of 3.46 x 10⁸ m from earth the gravitational field intensity will be zero.