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PhysicsJEE Main 21 Jan 2026, Shift 2·Q1·MCQ·Moderate

Electric Potential and Capacitance · Potential energy

Consider two identical metallic spheres of radius RR each having charge QQ and mass mm. Their centers have an initial separation of 4R4R. Both the spheres are given an initial speed of uu towards each other. The minimum value of u, so that they can just touch each other is : (Take k=14πϵ0k = \dfrac{1}{4\pi\epsilon_0} and assume kQ2>Gm2kQ^2 > Gm^2 where G is the Gravitational constant)
  1. (1)kQ24mR(1−Gm2kQ2)\sqrt{\dfrac{kQ^2}{4mR}\left(1 - \dfrac{Gm^2}{kQ^2}\right)}
  2. (2)kQ24mR(1+Gm2kQ2)\sqrt{\dfrac{kQ^2}{4mR}\left(1 + \dfrac{Gm^2}{kQ^2}\right)}
  3. (3)kQ22mR(1−Gm2kQ2)\sqrt{\dfrac{kQ^2}{2mR}\left(1 - \dfrac{Gm^2}{kQ^2}\right)}
  4. (4)kQ22mR(1−Gm22kQ2)\sqrt{\dfrac{kQ^2}{2mR}\left(1 - \dfrac{Gm^2}{2kQ^2}\right)}

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