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64 tiny drops of water having same radiu...

64 tiny drops of water having same radius and same charge are combined to form one large drop. The ratio of potential of the large drop to the small drop is

A

`4:1`

B

`1:4`

C

`16:1`

D

`1:16`

Text Solution

Verified by Experts

The correct Answer is:
C
Potential of one tiny drop, `V_(1) = 1/(4 pi epsilon_(0))q/r`
Now, charge of the large water drop = 64 q
Ratio of the volume of the tiny water drop to the volume of the large water drop = 1:64
Then, ratio of their radii = `1 : root(3)(64) = 1:4`
`:.` Potential of the large water drop,
`V_(2) = 1/(4 pi epsilon_(0))(64q)/(4r) = 16 V_(1), i.e., (V_2)/(V_1) = 16/1 = 16 : 1` .
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