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Q.

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 )

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a

v2=yqQ4π∈0RR+ym+g

b

v2=yqQ4π∈0R2ym+g

c

v2=2yqQ4π∈0RR+ym+g

d

v2=2yQqR4π∈0R+y3m+g

answer is C.

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Detailed Solution

Gain in kinetic energy = loss in potential energy​⇒KE= ΔUgravitational + ΔUelectric​⇒12mv2= mgy + kQqR- kQqR+y⇒12mv2= mgy + kQq1R-1R+y  ,where K=14π∈0⇒v2= 2yg+Qq4π∈0RR+ym
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