Gravitation · Question 14

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 2a and also the masses of the spheres are made 2 m, then they will collide after seconds.

Answer

8

Solution

The collapse time can depend only on G, m and a.

Acceleration of each sphere Gma2 and the distance to be covered a

t aGm/a2 = a3Gm

t'T = (2a)32m ma3 = 4 = 2

t' = 2 4 = 8 s

Answer: 8