Two small metallic spheres, each of mass m = 0.210 g, are suspended as pendulums

Question

Two small metallic spheres, each of mass m = 0.210 g, are suspended as pendulums by light strings of length L as shown in the figure below. The spheres are given the same electric charge of 6.6 nC, and they come to equilibrium when each string is at an angle of theta = 4.90degree with the vertical. How long are the strings? Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four digit accuracy to minimize roundoff error, m

Explanation / Answer

let T is the tension in the strings

as the sphere is in euqilibrium

Fnet,y = 0

T*cos(theta) - m*g = 0

T = m*g/cos(4.9)

= 0.21*10^-3*9.8/cos(4.9)

= 2.066*10^-3 N

Fnet,x = 0

T*sin(theta) - Fe = 0

Fe = T*sin(4.9)

k*q^2/r^2 = 0.1764*10^-3

r = q*sqrt(k/0.1764*10^-3)

= 6.6*10^-9*sqrt(9*10^9/0.1764*10^-3)

= 47.14*10^-3 m

from figure

r = 2*L*sin(4.9)

L = r/(2*sin(4.9))

= 47.14*10^-3/(2*sin(4.9))

= 0.276 m

= 27.6 cm

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