Two hard rubber spheres, each of mass m = 16.6 g, are rubbed with fur on a dry d

Question

Two hard rubber spheres, each of mass m = 16.6 g, are rubbed with fur on a dry day and are then suspended with two insulating strings of length L = 4.95 cm whose support points are a distance d = 3.03 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 = 10.3° with the vertical. Find the amount of charge on each sphere. (Enter your answers from smallest to largest.)

Two identical spheres, each of mass m, hang at the bottoms of two strings, each of length L. The tops of the strings are attached to the ceiling such that the top of one string is attached a distance of dto the right of the other. The left sphere and string are displaced to the left of vertical by an angle . The right sphere and string are displaced to the right of vertical by an angle .

Explanation / Answer

given two hard rubber spheres

mass = m = 16.6 g each

L = 4.95 cm

d = 3.03 cm

q1 = q

q2 = 2q

theta = 10.3 deg

then

let tension in the string be T

then from force balance

Tsin(theta) = 2kq^2/(d + 2Lsin(theta))^2

Tcos(theta) = mg

tan(theta) = 2kq^2/mg(d + 2Lsin(tehta))^2

putting values we get

q = 6.1617*10^-8 C

q1 = 6.1617*10^-8 C

q2 = 2q1 = 1.23 234*10^-7 C

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