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Two identical small insulating balls are suspended by separate 0.291m threads that are attached to a...

Two identical small insulating balls are suspended by separate 0.291m threads that are attached to a common point on the ceiling. Each ball has a mass of 7.90×10-4kg. Initially the balls are uncharged and hang straight down. They are then given identical positive charges and, as a result, spread apart with an angle of 35.0o between the threads. Determine the charge on each ball.

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Answer #1

r = distance between the two balls = 2 BC = 2 (0.291) Sin17.5 = 0.175 m

q = charge on each ball

m = mass of the ball = 7.9 x 10-4 kg

T = tension force in the string

using equilibrium of force in vertical direction

T Cos17.5 = mg

T = mg/Cos17.5                                                    eq-1

using equilibrium of force in horizontal direction

T sin17.5 = F

T Sin17.5 = k q2/r2

using eq-1

(mg/Cos17.5) Sin17.5 = k q2/r2

mg tan17.5 = k q2/r2

(7.9 x 10-4) (9.8) tan17.5 = (9 x 109) q2/(0.175)2

q = 9.11 x 10-8 C

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