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  3. A solid sphere of radius carries a charge  distributed uniformy over its volume. A very smal
# Engineering

A solid sphere of radius R carries a charge Q+q distributed uniformy 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 \nu when it has fallen through a vertical height y (see figure), then :(assume the remaining portion to be spherical ).
Option: 1 \nu ^{2}=y\left [ \frac{qQ}{4\pi \epsilon _{0}R^{2}ym}+g \right ]  
Option: 2 \nu ^{2}=y\left [ \frac{qQ}{4\pi \epsilon _{0}R(R+y)m}+g \right ]
Option: 3 \nu ^{2}=2y\left [ \frac{Qq\; R}{4\pi \epsilon _{0}(R+y)^{3}m}+g \right ]
Option: 4 \nu ^{2}=2y\left [ \frac{qQ}{4\pi \epsilon _{0}R(R+y)m} +g\right ]

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