The bodies of masses 100 ~kg and 8100 ~kg are held at a distance of 1 ~m . The gravitational field at a point on the line joining them is zero. The gravitational potential at that point in J / kg is (G=6.67 10⁻¹¹ Nm ^2 / kg ^2 )

Step-by-step solution

Mass of first body (m₁ )=100 ~kg Mass of second body (m₂ )=8100 ~kg Distance between two bodies =1 ~m Distance of null point from 100 ~kg aligned & x= d m₂ m₁ +1 & x= 1 8100 100 +1 aligned or, x= 1 8100 100 +1 or, aligned x & = 1 9+1 = 1 10 & =0.1 ~m aligned The gravitational potential at that point is given by aligned & =-G ( m₁ 0.1 + m₂ 0.9 ) & =-6.67 10⁻¹¹ ( 100 10⁻¹ + 8100 9 10⁻¹ ) & =-6.67 10⁻¹¹(1000+9000) & =-6.67 10⁻⁷ ~J / kg aligned