Question

Two equally charged insulating balls each weigh 0.16 g and hang from a common point by identical threads 35 cm long. The balls repel each other so that the separation between their centers is 6.8 cm.
What is the magnitude of the charge on each ball

Answer 1

Answer:

Q₁ = Q₂ = 8.84 x 10⁻⁹ C

Explanation:

given,

mass of ball, m = 0.16 g = 1.6 x 10⁻⁴ Kg

ball each other, r = 6.8 cm

Weight of the ball

F_w = m g

F_w = 1.6 x 10⁻⁴ x 9.8

F_w = 1.56 x 10⁻³ N

The tension in each string is a force directed along the length of the string and is the hypotenuse of a right triangle.

we have to find the horizontal component of the forces.

The length of the string,L is 35 cm so, it will be the hypotenuse.

θ be the angle made with imaginary vertical line and the string.

now,

$sin \theta = \dfrac{r\2}{L}$

$sin \theta = \dfrac{3.4}{35}$

   θ = 5.57°

horizontal component of the force = ?

vertical component of force,F_v = 1.56 x 10⁻³ N

$tan\theta = \dfrac{F_H}{F_v}$

$tan(5.57^0) = \dfrac{F_H}{1.56\times 10^{-3}}$

 F_h = 1.52 x 10⁻⁴ N

now, each ball will be repelled by

F = 1.52 x 10⁻⁴ N

now calculation of charges

$F = \dfrac{kQ_1Q_2}{r^2}$

Q₁ = Q₂ because both charge are same

$1.52\times 10^{-4} = \dfrac{9\times10^9Q^2}{0.068^2}$

    Q² = 7.809 x 10⁻¹⁷

   Q = 8.84 x 10⁻⁹ C

hence the change on the balls were Q₁ = Q₂ = 8.84 x 10⁻⁹ C