The distance between the centre of moon and earth is (D ) and mass of earth is 81 times the mass of moon. At what distance from the centre of the earth, the gravitational force will be zero?

Step-by-step solution

Let a unit mass (m ) is present at a distance (x ) from the earth, where gravitational force is zero. ( G m M_e x^2 = G m M (D-x)^2 )...(i) where, (M_e ) is mass of earth and (M ) is mass of moon. Given, (M_e=81 M ) ( ) From Eq. (i), we have ( aligned & G m 81 M x^2 = G m M (D-x)^2 81 x^2 = 1 (D-x)^2 & ( 9 x )^2= 1 (D-x)^2 9 x = 1 D-x & 9 D-9 x=x 9 D=10 x & x= 9 D 10 aligned )