`1000` small water drops each of raius `r` and charge `q` coalesce together to form one spherical drop.
(A) the ratio of capacitances of big and small drop is `10`
(B) the ratio of potential of big and small drop is `100`
(c) the ratio of surface charge densities of big and small drop is `10`
(D) the ratio of energy stored of big and small drop is `10^(5)`

Options

A. `A,B`
B. `A,B,C`
C. `A,C,D`
D. `A,B,C,D`

Answer

D

Explanation

Let R : radius of big drop
`Q:` charge on big drop
`Q=1000q`
Since volume remains same
`(4)/(3)piR^(3)=1000xx(4)/(3)pir^(3)impliesR=10r`
(A) Ratio of capacitance `(c)/(C')=(4piin_(0)R)/(4piin_(0)r)=(R )/(r )=10`
(B) Ratio of potentials
`(V)/(V')=((1)/(4piin_(0))(Q)/(R ))/((1)/(4piin_(0))(q)/(r ))=((Q)/(q))((r )/(R ))=1000xx(1)/(10)=100`
(c) Ratio of surface chrge densities
`(sigma)/(sigma')=(Q//4piR^(2))/(Q//4pir^(2))=((Q)/(q))((r )/(R ))^(2)=1000xx(1)/(100)=10`
(D) Ratio of energy stored `(U)/(U')=(Q^(2)//2C')/(q^(2)//2C')=((Q)/(q))^(2)((c)/(C'))`
`=(1000)^(2)xx(1)/(10)=10^(5)`