A solid sphere of radius R carries a charge Q + q distributed… | JEE Main 2020 (5 Sep, Shift 1)

Q48JEE Main 2020 · 5 SEP · SHIFT 1Difficult

Electrostatic Potential Energy

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 from the bottom of the sphere and falls down vertically under gravity. This piece carries charge q. If it acquires a speed v when it has fallen through a vertical height y (see figure), then:

(assume the remaining portion to be spherical).

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Answer: (c)

The remaining sphere has charge $Q$ ; outside it $V = \frac{kQ}{r}$ .
Energy: $\frac{1}{2}mv^2 = mgy + kqQ\left(\frac{1}{R} - \frac{1}{R+y}\right) = mgy + \frac{kqQ\,y}{R(R+y)}$
$v^2 = 2y\left[\frac{qQ}{4\pi\varepsilon_0 R(R+y)m} + g\right]$
So the answer is (c).

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Electrostatic Potential Energy question from JEE Main 2020 (5 Sep, Shift 1)

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