Two hard rubber spheres, each of mass m = 13.9 g, are rubbed with fur on a dry d

Question

Two hard rubber spheres, each of mass m = 13.9 g, are rubbed with fur on a dry day and are then suspended with two insulating strings of length L = 4.50 cm whose support points are a distance d = 3.27 cm from each other as shown in the figure below. During the rubbing process, one sphere receives exactly twice the charge of the other. They are observed to hang at equilibrium, each at an angle of = 10.6° with the vertical. Find the amount of charge on each sphere. (Enter your answers from smallest to largest.)

Explanation / Answer

here,

mass of spheres , m = 13.9 * 10^-3 kg

L = 0.045 m

d = 0.0327 m

charge on spheres , are q1 = q and q2 = 2 * q

theta = 10.6 degree

the electrstatic froce , F = k * q1 * q2 / (d + 2* L * sin(theta))^2

let the tension in the strings be t

forone sphere,

t * cos(theta) = m * g ...(1)

and

t * sin(theta) = F ....(2)

from (1) and (2)

tan(theta) = F /mg

tan(10.6) = k * q1 * q2 / ( m * g *(d + 2* L * sin(theta))^2)

tan(10.6) = 9 * 10^9 * 2 * q^2 /( 0.0139 * 9.8* ( 0.0327 +2 * 0.045 * sin(10.6) )^2)

q = 5.86 * 10^-8 C

therefore charges are 5.86 * 10^-8 C and 11.72 * 10^-8 C

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