Question

Two small metallic spheres, each of mass m-0.40 g, are suspended as pendulums by light strings from a common point as shown in the figure below. The spheres are given the same electric charge, and it is found that they come to equilibrium when each string is at an angle of θ = 7.5° with the vertical. If each string has length L 28.0 cm, what is the magnitude of the charge on each sphere? nC

Answer 1

Solution)

Force due to gravity,

is 0.0004 kg * 9.8 m/s^2 = 0.00392 N

To keep string at 7.5 degree angle from the vertical the horizontal force on either sphere will be

0.00392 N * tan (7.5 degrees) = 0.000516 N

The distance between the spheres will be

2 * 30 cm * sin(7.5 degrees) = 0.078 m

Now,

F = kQ1Q2/r^2,

where k = 9 x 10^9 Nm^2/C^2

On substituting values, we have

Q^2 = 0.000516 N * (0.078 m)^2 / (9x10^9Nm^2/C^2)

Q = 1.86 * 10^-8 C = 0.0186 * 10^-9 nC (Ans)

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Good luck!:)