Consider two identical metallic spheres of radius 
each having charge 
and mass 
. Their centers have an initial separation of 
. Both the spheres are given an initial speed of 
towards each other. The minimum value of 
, so that they can just touch each other is : (Take 
and assume 
where 
is the Gravitational constant)
Text Solution
Verified by ExpertsB
Using energy conservation, the system's kinetic energy must overcome the increase in electrostatic potential energy as the spheres approach.
Initial state: separation 4R, speed u each.
Final state: touching (separation 2R), speed zero.
Change in potential energy: 
.
Initial kinetic energy: 
.
Energy equation: 
.
Therefore, 
.
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