Q 12-02-038JEE MainJEE Main 2026 (6 Apr, Shift 2)Medium
A sphere of capacitance $100$ pF is charged to a potential of $100$ V. Another identical uncharged metal sphere is brought in contact with the charged sphere, then the change in the total energy stored on these spheres, when they touch is $\alpha \times 10^{-7}$ J. The value of $\alpha$ is ______. (combined capacitance of spheres is $200$ pF)
Answer: (B) $\dfrac{5}{2}$
Concept. Charge is shared; compare $\dfrac{Q^2}{2C}$ before and after.
Step 1. Before. $5 \times 10^{-7}$ J, $Q = 10^{-8}$ C.
Step 2. After. $\dfrac{10^{-16}}{4 \times 10^{-10}} = 2.5 \times 10^{-7}$ J.
Step 3. Change. $2.5 \times 10^{-7}$ J: $\alpha = \dfrac52$.
Answer. $\dfrac52$ (Option B).
Solution by Sreeraj P, M.Sc Physics
