Question

Two bodies P and Q having masses 2kg and 4kg respectively are seperated by 2m. Where should another body, R, weighing 1kg be kept so that the gravitational force on R due to P and Q is zero​

Answer 1

Answer:Given data-

                  1. 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) final ans

Explanation:

Answer 2

Explanation:

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