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).

Question

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).

v² = $y\left[ {{{qQ} \over {4\pi {\varepsilon _0}R\left( {R + y} \right)m}} + g} \right]$

v² = $2y\left[ {{{qQR} \over {4\pi {\varepsilon _0}{{\left( {R + y} \right)}^3}m}} + g} \right]$

v² = $2y\left[ {{{qQ} \over {4\pi {\varepsilon _0}R\left( {R + y} \right)m}} + g} \right]$

v² = $y\left[ {{{qQ} \over {4\pi {\varepsilon _0}{R^2}ym}} + g} \right]$

Solution

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