Each question is worth 10%. In order to receive credits, you must show ALL your

Question

Each question is worth 10%. In order to receive credits, you must show ALL your work. Two hard rubber spheres, each of mass m = 14.5 g, are rubbed with for on a dry day and are then suspended with two insulating strings of length L = 5.20 cm whose support points are distance d = 2.97 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 theta = 10.3 degree with the vertical. Find the amount of charge on each sphere.

Explanation / Answer

Here,

m = 14.5 gm = 0.0145 Kg

theta = 10.3 degree

let the charge on each spehere is q

electric force/gravity = tan(theta)

9 *10^9 * q^2/(2 * 0.052 * sin(10.3 degree) + 0.0297)^2 = tan(10.3 degree) * 0.0145 * 9.8

solving for q

q = 8.18 *10^-8 C

the charge on each sphere is 8.18 *10^-8 C

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