Question

Two pith-balls each wieghing 10-3 kg are suspended from the same point by means of silk thread 0.5 m long. On charging the pith balls equally, they found to repel each other to distance of 0.2 m .Calculate the charge on each ball?

Answer 1

Let tension in the string be T

So mg=Tcosθ

Repulsive force F & weight of the balls are perpendicular to each other.

Therefore,

(F/mg)= tanθ

F=mg tanθ

From the figure, sinθ= 0.1/0.5= 1/5

cosθ=√(1-sin²θ)

         = √(24/25)

tanθ=(1/5)/{√(24/25)}

       =0.2

F= 10⁻³×9.8×0.2

 = 1.96×10⁻³N

We know that, Electrostatic force, F= kq²/r²

           q²=(F×r²)/k

              = (1.96×0.2×0.2)/(9×10⁹)

              = √(8.7×10⁻¹²)

              = 2.95 μC

Answer 2

According to the fig.

force of repulsion is balanced by the sin component of the tension in the string.

F = Tsinθ

Weight is balanced by the cos component of the tension.

mg = Tcosθ

Fmg = tanθ

F = mg tanθ

sinθ = 0.10.5

sinθ = 1/5

cos θ = 2425

secθ = 2524

tanθ = 0.2

F = 1.96×10−3 N

F= kq2/r2

q2 = Fr2/k = 1.96×10−3×0.2×0.2/9×10^9

q = 0.9 μC