Consider two identical metallic spheres of radius R each having charge Q and mass m. Their centers have an ini…

Question

Consider two identical metallic spheres of radius $$R$$ each having charge $$Q$$ and mass $$m$$. Their centers have an initial separation of $$4R$$. Both the spheres are given an initial speed of $$u$$ towards each other. The minimum value of $$u$$, so that they can just touch each other is :
(Take $$k = \frac{1}{4 \pi \epsilon_0}$$ and assume $$kQ^2 > Gm^2$$ where $$G$$ is the Gravitational constant)

Accepted Answer

A. $$\sqrt{\frac{kQ^2}{4mR} \left( 1 - \frac{Gm^2}{kQ^2} \right)}$$

Answer

B. $$\sqrt{\frac{kQ^2}{2mR} \left( 1 - \frac{Gm^2}{kQ^2} \right)}$$

Answer

C. $$\sqrt{\frac{kQ^2}{2mR} \left( 1 - \frac{Gm^2}{2kQ^2} \right)}$$

Answer

D. $$\sqrt{\frac{kQ^2}{4mR} \left( 1 + \frac{Gm^2}{kQ^2} \right)}$$

Answer & step-by-step solution

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