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 
seconds. If the sides of the triangle are increased to length 
and also the masses of the spheres are made 2 m, then they will collide after 
seconds.
Text Solution
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(8)
Dimensional Analysis:
Using dimensional analysis for gravitational interactions, we have:
Where G has dimensions 
.
Solving for Exponents:
Equating dimensions, we solve:
Time Proportionality:
Which simplifies to:
Applying New Conditions:
When the side length becomes 2a and mass becomes 2m :
Simplifying:
Thus, the spheres will collide after 8 seconds under the new conditions.
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