Question

Two identical pith balls are charged by rubbing one against the other. They are suspended from a horizontal rod through two strings of length 20 cm each, the separation between the suspension points being 5 cm. In equilibrium, the separation between the balls is 3 cm. Find the mass of each ball and the tension in the strings. The charge on each ball has a magnitude 2.0 × 10⁻⁸ C.

Answer 1

 

As given, q = 2 × 10^-8 and r = 3 cm = 3 × 10^-2m

Force between two charged particles

∵ `F = (kq_1q_2)/r^2`

= `(9 xx 10^9 xx 2 xx 10^-8 xx 2 xx 10^-8)/((3 xx 10^-2)^2)`

= 4 × 10^-3H
from Fig T sin θ = F   ...(i)

T cos θ = mg   ...(ii)

Tan θ = `F/(mg)`

Here, Tan θ = `P/B = 1/sqrt399 ≈ 1/20`

and `1/20 = F/(mg)`

m = `(20F)/g`

m = 8 g

T = `F/sin θ`

= `(4 xx 10^-3)/(1/20)`

= 8 × 10^-2 N