Consider two identical metallic spheres of radius R ea... | null (Physics) | DivineJEE

JEE Mains 2026 21st January Shift 2

Physics

Consider two identical metallic spheres of radius

R

each having charge

Q

and mass

m

. Their centers have an initial separation of

4 R

. 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

k Q^{2}>G m^{2}

where G is the Gravitational constant)

\sqrt{\frac{k Q^{2}}{4 m R}\left(1-\frac{G m^{2}}{k Q^{2}}\right)}

\sqrt{\frac{k Q^{2}}{4 m R}\left(1+\frac{G m^{2}}{k Q^{2}}\right)}

\sqrt{\frac{k Q^{2}}{2 m R}\left(1-\frac{G m^{2}}{k Q^{2}}\right)}

\sqrt{\frac{k Q^{2}}{2 m R}\left(1-\frac{G m^{2}}{2 k Q^{2}}\right)}

Correct Answer:

Using energy conservation

\\

(2)

\left(\frac{1}{2} m u^{2}\right)-\frac{G m^{2}}{4 r}+\frac{K Q^{2}}{4 r}=-\frac{G m^{2}}{2 r}+\frac{K Q^{2}}{2 r}\\

u=\sqrt{\frac{1}{4 m r}\left(K Q^{2}-G m^{2}\right)}

Select an option to instantly check whether it is correct or wrong.

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