Question

two point of masses having mass M and 4m are placed at distance R the gravitational potential at a point where gravitational field intensity is zero

Answer 1

Dear Sam! Thanks for putting your doubt.

Let the masses M and 4M be kept a distance r from each other as shown in the attached image. We are given that the gravitational field intensity of the point where the gravitational potential has to be found is zero. Let it be somewhere on the line r.

Now, we know by a quick formula, to find a point (x) where the gravitational field intensity is zero as;

               x = r / √n + 1

So, finding the value of the point where the gravitational field intensity is zero.

     x = r/ √n + 1

     x = r/ √4 + 1

     x = r/ 2 + 1

     x = r/ 3

So till the distance x from mass M, the gravitational field intensity is zero. Also, the remaining distance becomes 2r/ 3.

Now, for gravitational potential from both the masses to the given point can be written as;

     

   v = - GM/ r - GM/r

   v = - GM/ r/3  - 4 GM/ 2r/3

   v = - 3 GM/r - 6 GM/ r

   v = - 9 GM/r

Hence, the gravitational potential at a point where the gravitational field intensity is zero is - 9 GM/r.