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

Answer 1

Answer is : (8)

As limiting case of elliptical path is straight line therefore proportionality \(T^2 \propto \frac{a^3}{M}\) will holds from

\(\left(T^2 = \frac{4 \pi^2}{GM}r^3\right)\)

\(\frac{4^2}{T^2} = \frac{a^3}{m} \cdot \frac{2m}{(2a)^3} = \frac{2}{8} = \frac{1}{4}\)

\(\frac{4}{T} = \frac{1}{2}\)

T = 8 seconds