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Q. Eight identical spherical mercury drops charged to a potential of 20V each are coalesced into a single spherical drop

(1) The internal Energy of the system remains the same
(2) The new potential of the drop is 80V
(3) Internal Energy of the system decreases
(4) The potential remains the same i.e. 20V

Answer 1

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Syeda answered 10 month(s) ago

Q.Eight identical spherical mercury drops charged to a potential of 20V each are coalesced into a single spherical drop (1) The internal..

Q. Eight identical spherical mercury drops charged to a potential of 20V each are coalesced into a single spherical drop

(1) The internal Energy of the system remains the same
(2) The new potential of the drop is 80V
(3) Internal Energy of the system decreases
(4) The potential remains the same i.e. 20V

Class-X Physics

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Asked by G

Oct 9

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Janhavi , SubjectMatterExpert

Member since Feb 20 2013

Let r and R be the radii of the individual mercury drop and the coalesced 
drop. 
Volume of the coalesced drop = 4πR3/3 = 8 x 4πr3/3 
⇒ R = 2r.
Let q be the charge on each mercury drop and Q = 8q be the charge on the coalesced drop.

V = kq/r = 20 V
V' = kQ/R
    = k. 8q/(2r)
    = 4 kq/r 
    = 4 x 20 V = 80 V.

So the answer is (2) The new potential of the drop is 80 V.
    

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Syeda , SubjectMatterExpert

Member since Jan 25 2017

Answer.

    Let r and R be the radii of the individual mercury drop and the coalesced 
drop. 
Volume of the coalesced drop = 4πR3/3 = 8 x 4πr3/3 
⇒ R = 2r.
Let q be the charge on each mercury drop and Q = 8q be the charge on the coalesced drop.

V = kq/r = 20 V
V' = kQ/R
    = k. 8q/(2r)
    = 4 kq/r 
    = 4 x 20 V = 80 V.

So the answer is (2)