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Two identical very small metal spheres, ...

Two identical very small metal spheres, A and B, that are electrically neutral are fixed at a distance R On insulating handles. A third identical sphere C carrying charge Q is also connected to an insulating handle. C ia first brought into contact with A and B and then moved away from these two spheres. It is found that A and B apply `F_1` force on each other.
Now C with the remaining charge is again brought into contact with A and then moved away from A and B. It is found that A and B apply `F_2` force on each other. Now C is further brought into contact with B and then moved away from A and B. It is found that A and B apply `F_3` force on each other Finally B is moved closer to A at a distance r, such that the force between them again becomes `F_1`.
The magnitude of `F_2//F_3` is

A

`3//4`

B

`4//3`

C

`4//5`

D

`5//4`

Text Solution

Verified by Experts

The correct Answer is:
C
Charge acquired by B when C touches it for the second time
`q_4=1/2("3Q"/8+Q/4)="5Q"/16`
Force between A and B :
`F_3=1/(4piepsilon_0)(("3Q"/8)("5Q"/16))/R^2 =15/128 1/(4piepsilon_0) Q^2/R^2` …(iii)
`F_2/F_3=3/32xx128/15=4/5`
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