$A$ 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
  $v^{2}=2 y\left[\frac{q Q}{4 \pi \epsilon_{0} R(R+y) m}+g\right]$
• B
  $v^{2}=y\left[\frac{q Q}{4 \pi \epsilon_{0} R^{2} y m}+g\right]$
• C
  $v^{2}=2 y\left[\frac{q Q R}{4 \pi \epsilon_{0}(R+y)^{3} m}+g\right]$
• D
  $v^{2}=y\left[\frac{q Q}{4 \pi \epsilon_{0} R(R+y) m}+g\right]$