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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).
(a)
\[
v^{2}=y\left[\frac{q Q}{4 \pi \varepsilon_{0} R(R+y) m}+g\right]
\]
(b)
\[
v^{2}=2 y\left[\frac{q Q R}{4 \pi \varepsilon_{0}(R+y)^{3} m}+g\right]
\]
(c) \( v^{2}=y\left[\frac{q Q}{4 \pi \varepsilon_{0} R^{2} y m}+g\right] \)
(d) \( v^{2}=2 y\left[\frac{q Q}{4 \pi \varepsilon_{0} R(R+y) m}+g\right] \)
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