The centres of two identical spheres are `50 cm` apart. If the gravitational force between the spheres be `4.0 N`, find the mass of each sphere. Given, `G = 6.67 xx 10^(-11) Nm^(2)kg^(-2)`.

Options

A. `2 xx 10^(6) kg`
B. `1.22 xx 10^(8) kg`
C. `4 xx 10^(3) kg`
D. `1.22 xx 10^(5) kg`

Answer

D

Explanation

Let `m` be the mass of each sphere.
Then, `r = 50 cm = 0.50m , F = 4.0 N`.
`F = G (m xx m)/(r^(2))` or `m = sqrt((F r^(2))/(G)) = sqrt((4 xx (0.5)^(2))/(6.67 xx 10^(-11))`
`= 1.22 xx 10^(5) kg`