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muminat
3 years ago
12

Two equally charged insulating balls each weigh 0.16 g and hang from a common point by identical threads 35 cm long. The balls r

epel each other so that the separation between their centers is 6.8 cm.
What is the magnitude of the charge on each ball
Physics
1 answer:
Dafna11 [192]3 years ago
5 0

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

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