1.

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

Answer»

`3//4`
`4//3`
`4//5`
`5//4`

Solution :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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