$A$ hollow metal sphere of radius $15 \,cm$ is charged such that the potential on its surface is $20 \,V$. Then, the potential at the centre of the sphere is (in $V$)

$m$ દળ અને $q$ વિદ્યુતભાર ધરાવતી એક ગોળીને $R$ ત્રિજ્યા અને કુલ $+q$ વિદ્યુતભાર ધરાવતા સમાન રીતે વિદ્યુતભારીત નક્કર ગોળા તરફ છોડવામાં આવે છે. જો તે $u$ ઝડપ સાથે ગોળાની સપાટી પર અથડાય,તો ગોળામાંથી પસાર થવા માટે જરૂરી લઘુત્તમ ઝડપ $u$ શોધો. (સ્થિત વિદ્યુત બળો સિવાય ગોળી પર લાગતા તમામ અવરોધક બળો અથવા ઘર્ષણને અવગણો.)

$(a)$ Calculate the potential at a point $P$ due to a charge of $4 \times 10^{-7} \; C$ located $9 \; cm$ away.
$(b)$ Hence,obtain the work done in bringing a charge of $2 \times 10^{-9} \; C$ from infinity to the point $P$. Does the answer depend on the path along which the charge is brought?

Inside a hollow charged spherical conductor,the potential

Given below are two statements $:$ one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A :$ Work done in moving a test charge between two points inside a uniformly charged spherical shell is zero,no matter which path is chosen.
Reason $R :$ Electrostatic potential inside a uniformly charged spherical shell is constant and is same as that on the surface of the shell.
In the light of the above statements,choose the correct answer from the options given below.

Two points $P$ and $Q$ are maintained at the potentials of $10\, V$ and $-4\, V$,respectively. The work done in moving $100$ electrons from $P$ to $Q$ is: