Physics · 2020
JEE Main · 5 September 2020, Shift 1 · Q11
A solid sphere of radius R carries a charge Q + q distributed uniformly over its volume. A very small point like piece of it of mass m gets detached…
A solid sphere of radius $\displaystyle R$ carries a charge $\displaystyle \mathrm{Q}+\mathrm{q}$ distributed uniformly over its volume. A very small point like piece of it of mass m gets detached from the bottom of the sphere and falls down vertically under gravity. This piece carries charge q. If it acquires a speed $\displaystyle v$ when it has fallen through a vertical height $\displaystyle y$ (see figure), then : (assume the remaining portion to be spherical).

Official answer
(3)
$\displaystyle v^2=2 y\left[\frac{\mathrm{qQ}}{4 \pi \epsilon_0 \mathrm{R}(\mathrm{R}+y) \mathrm{m}}+\mathrm{g}\right]$
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JEE Main 2020 Physics question, with the answer from NTA’s final answer key. Where our answers come from.