Question

Two bodies A and B having masses 2 kg and 4 kg respectively are separated by 2 m.
Where should a body of mass 1 kg be placed so that the gravitational force on this body due to bodies A and B is zero?

Answer 1

Explanation:

Mass  A = 2Kg

                 2) Mass B = 4Kg

                  3) Mass C=  1kg

                   Distance between the bodies = 2mtr

Now we are required to find  a point between these 2 masses where if a small mass of 1Kg is put then NET  gravitational force on it exerted by remaining other 2 masses will be zero

              

             Formula of gravitational force between 2 objects is given by:

                                   G M₁ M₂ / [distance between them]²

            where,

                          G= Gravitational constant

                           M₁ and M₂ are masses

now assume mass c is put somewhere between A ans B such that net gravitational force is zero and also distance of C from A is X meter

 therefore remaining distance of C from B will be  (2-X)

In Other words ,

 force between A-C = force between C-B

        G M(A) * M(C)/ X²  = G M(C) * M(B) / [2-X]²

         after cancelling equal terms we will be left with this:

            M(A) /M(B)  = X²/[2-X]²

            2/4  = X²/[2-X]² =>    1/2 =   X²/[2-X]²

         taking both sides under root

           1/√2 = X/ (2-X) =>     2-X = √2 X

           2 = √2 X- X  or  X(2-√2) = 2

             X = (1 - 1/√2)

Hope it helps!

Answer 2

Answer:

Mass  A = 2Kg

                2) Mass B = 4Kg

                 3) Mass C=  1kg

                  Distance between the bodies = 2mtr

Now we are required to find  a point between these 2 masses where if a small mass of 1Kg is put then NET  gravitational force on it exerted by remaining other 2 masses will be zero

             

            Formula of gravitational force between 2 objects is given by:

                                  G M₁ M₂ / [distance between them]²

           where,

                         G= Gravitational constant

                          M₁ and M₂ are masses

now assume mass c is put somewhere between A ans B such that net gravitational force is zero and also distance of C from A is X meter

therefore remaining distance of C from B will be  (2-X)

In Other words ,

force between A-C = force between C-B

       G M(A) * M(C)/ X²  = G M(C) * M(B) / [2-X]²

        after cancelling equal terms we will be left with this:

           M(A) /M(B)  = X²/[2-X]²

           2/4  = X²/[2-X]² =>    1/2 =   X²/[2-X]²

        taking both sides under root

          1/√2 = X/ (2-X) =>     2-X = √2 X

          2 = √2 X- X  or  X(2-√2) = 2

            X = (1 - 1/√2)

YUP THATS YOUR ANSWER

Explanation: