Question

Four particles of masses m ,2m,3m,4m are kept in sequence ah the corner of a square of side a . the magnitude of gravitational force acting on particle of mass m placed at the center of the square will be

Answer 1

Answer:

The net force acting on O = 4√2Gm²/a²

Explanation:

Four particles of masses m, 2m, 3m , 4m are kept in sequence at the corners of a square of side a. A particle of mass m is placed at centre O of square.  

Now calculate the force exerted by A on O = Gm²/(a/√2)² = 2Gm²/a²  

The force exerted by B on O = 2Gm²/(a/√2)²  

= 4Gm²/a²

Now the force exerted by C on O = 3Gm²/(a/√2)² = 6Gm²/a²

The force exerted by D on O = 4Gm²/(a/√2)²

= 8Gm²/a²

Let us consider F = 2Gm²/a²

Then the force exerted by A on O = F

Force exerted by B on O = 2F

Force exerted by C on O = 3F

Force exerted by D on O = 4F

See figure , resultant force of B and D (along CO ) = 4F - 2F = 2F

Now resultant force of A and C ( along DO ) = 3F - F = 2F  

Now, net force acting on O = √{(2F)² + (2F)²} = 2√2F

Putting F = 2Gm²/a²

 Hence net force acting on O = 4√2Gm²/a²