(a) Let the charged sphere is A and uncharged sphere is B. We know charge distribute equally on two identical spheres if both spheres come in contact. So touch sphere A with B, final charges will be 1/2 and 1/2 on both spheres. Now touch sphere B to ground this will neutralize the sphere B. Touch B to A again, now 1/2 will distribute on both spheres equally again resulting in 1/4 and 1/4 charge on both spheres. Again touch B to ground to neutralize it. Touch B to A again, this time ffinal charge on both spheres will be 1/8 and 1/8. Touch B to ground. So now charge on B is 0 and charge on A is 1/8 microC.
(b) We will need 3 uncharged identical spheres(let B, C, D). First A and B are touched to each-other giving 1/2 and 1/2 charge on A and B. Now A to C giving 1/4 and 1/4 charge on A and C. Now A to D giving 1/8 and 1/8 microC on A and D. So finally we will have A with 1/8microC chrage.
(c) We will need 2 uncherged identical spheres (B and C). So, charge on spheres is A=1microC, B=0, C=0. Now follow the steps (A+B means A and B touched to each-other)-
A+B=1/2 on A and 1/2 on B (So we will have A=1/2, B=1/2, C=0)
B+C=1/4 on each (we will have A=1/2, B=1/4, C=1/4)
A+C=3/8 on each (we will have A=3/8, B=1/4, C=3/8)
A+B=5/16 on each (we will have A=5/16, B=5/16, C=3/8)
So this is how we can get sphere A with 5/16microC.
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