Four identical particles of mass m are kept at the four corners of a square. If the gravitational force exerted on one of the masses by the other masses is 2 2 + 1 32 G m 2 L 2 , the length of the sides of the square is

Step-by-step solution

Resultant force, F n e t = 2 F + F ' , where F = G m 2 a 2 and F ' = G m 2 2 a 2 Therefore, F n e t = 2 G m 2 a 2 + G m 2 2 a 2 Comparing with the expression given in the question, we get 2 2 + 1 32 G m 2 L 2 = G m 2 a 2 2 2 + 1 2 ⇒ a = 4 L