Question

Two masses M and 4M are separated by a distance d. What will be the distance of mass 1 kg from M and 4M respectively, so that net gravitational force on it is zero?

Answer 1

Vinod that Newton's law of gravitation in mathematical form is equal to

F= GMm/r^2 ............ (1)

here F equals to 1 Newton (given )

trains between them is made twice then

F' = GMm/(2r)^2

= GMm/4r^2

comparing 1 and 2

F = 0.25*1 =0.25N

Answer 2

Dear student,

Given :-

• two masses = m and 4m
• distance between them = d
• new mass = m

To find :-

• the distance between them so that the net gravitational force on it is zero.

Solution :-

Let the required distance be x from mass m on the line having a distance of d. Since the net external force on the system is zero. Hence, the forces applied by them equal to each other i.e. f₁ = f₂.

Distance where a new mass is kept to equate the gravitational forces acting on it from both the masses kept on d is x. So, other length becomes d - x.

Hence, equating the forces on new mass kept at x exerted by the other two masses and can be given by;

     Gmm'/x²= Gm'nm/(d-x)²  

(where n represents magnitude)

     Gmm'/x²= Gm'4m/(d-x)²

      (d -x)²/x² = 4

      (d - x)/ x = √4

      d = √4 x + x

      d = x(√4 + 1)

      x = d/√4 + 1

      x = d/2 + 1

      x = d/3

Hence, the distance of mass m from new mass and 4m such that the gravitational force on new mass by the other mass comes to be zero is d/3.