A solid sphere of radius R carries total charge Q + q uniformly throughout its volume. A very small piece of mass m detaches from the bottom and falls vertically under gravity. The piece carries charge q. If its speed after falling a vertical distance y is v, which relation is correct? Assume the remaining charged body remains spherical.

Options

• Option A

  $v^2=2y\left\lbrack\frac{qQ}{4\pi\epsilon_{\omicron}R\left(R+y\right)m}+g\right\rbrack$

• Option B

  $v^2=y\left\lbrack\frac{qQ}{4\pi\epsilon_{\omicron}R^2ym}+g\right\rbrack$

• Option C

  $v^2=2y\left\lbrack\frac{qQR}{4\pi\epsilon_{\omicron}\left(R+y\right)^3m}+g\right\rbrack$

• Option D

  $v^2=y\left\lbrack\frac{qQ}{4\pi\epsilon_{\omicron}R\left(R+y\right)m}+g\right\rbrack$