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$$ I figure $$) 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$$ I figure $$) then : $$($$ assume the remaining portion to be spherical $$)$$

Infinity Learn · Accepted Answer

Gain in kinetic energy $$=$$ loss in potential energy​⇒$$KE$$$$=$$ ΔUgravitational $$+$$ ΔUelectric​⇒$$12mv2=$$ mgy $$+$$ $$kQqR-$$ $$kQqR+y$$⇒$$12mv2=$$ mgy $$+$$ $$kQq1R-1R+y$$  ,where $$K=14$$π∈$$0$$⇒$$v2=$$ $$2yg+Qq4$$π∈$$0RR+ym$$

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