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Grade: 11
        

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

one month ago

Answers : (1)

Arun
22984 Points
							
Four particles of masses m, 2m, 3m , 4m are kept in square ABCD at the corners of a square of side a. a particle of mass m is placed at centre O of square.
 
now, force exerted by A on O = Gm²/(a/√2)² = 2Gm²/a²
 
force exerted by B on O = 2Gm²/(a/√2)²
 
= 4Gm²/a²
 
force exerted by C on O = 3Gm²/(a/√2)² = 6Gm²/a²
 
force exerted by D on O = 4Gm²/(a/√2)²
 
= 8Gm²/a²
 
Let us consider F = 2Gm²/a²
 
then, 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= 4F - 2F = 2F along CO
 
and resultant force of A and C = 3F - F = 2F along DO
 
now, net force acting on O = √{(2F)² + (2F)²} = 2√2F
 
putting F = 2Gm²/a²
 
so, net force acting on O = 4√2Gm²/a²
 
 
one month ago
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