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Q.

Two identical small charged spheres A and B , each carrying a charge Q are suspended from a point O by two light non-conducting strings each of length l = 1m. Equilibrium separation between the spheres is found to be 10 mm. Now some more charge is supplied to the spheres so that charge on each sphere becomes 8Q. Then new equilibrium separation between the spheres is

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a

60 mm

b

80 mm

c

20 mm

d

40 mm

answer is D.

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Detailed Solution

(4)T  sinθ=F=14πε0 Q2x2T  cosθ= mg∴   tanθ= Q24πε0mg.  x2Since  x  <  <  l,  tanθ  ≈  sinθ =x/2l∴   x2l=Q24πε0mg x2. ⇒   x=Q2/3 .  l2πε0mg1/3 ⇒  x   ∝  Q2/3 ∴   x2x1=Q2Q12/3  ⇒   x210 =  8QQ2/3=4⇒   x2=40  mm
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Two identical small charged spheres A and B , each carrying a charge Q are suspended from a point O by two light non-conducting strings each of length l = 1m. Equilibrium separation between the spheres is found to be 10 mm. Now some more charge is supplied to the spheres so that charge on each sphere becomes 8Q. Then new equilibrium separation between the spheres is