Three identical spheres of mass m , are placed at the vertices of an equilateral triangle of length a. When released, they interact only through gravitational force and collide after a time T = 4 seco

Question

Three identical spheres of mass m , are placed at the vertices of an equilateral triangle of length a. When released, they interact only through gravitational force and collide after a time T = 4 seconds. If the sides of the triangle are increased to length 2 a and also the masses of the spheres are made 2 m , then they will collide after _____ seconds.

TestHub · Accepted Answer

​ T ∝ m x G y a z T ∝ M x [ M − 1 L 3 T − 2 ] y [ L ] z T ∝ M x − y L 3 y + z T − 2 y x − y = 0 ⇒ x = y − 2 y = 1 ⇒ y = − 2 1 ​ , x = − 2 1 ​ ⇒ 3 y + z = 0 z = − 3 y = 2 3 ​ ​ Hence ​ T ∝ m − 1/2 G − 1/2 a 3/2 T ∝ ( m a 3 ​ ) 1/2 T = 4 × ( 2 2 3 ​ ) 1/2 = 8 s ​

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