Two small metallic spheres, each of mass m = 0.190 g, are suspended as pendulums
ID: 2127802 • Letter: T
Question
Two small metallic spheres, each of mass m = 0.190 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 7.0 nC, and they come to equilibrium when each string is at an angle of ? = 5.20
Two small metallic spheres, each of mass m = 0.190 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 7.0 nC, and they come to equilibrium when each string is at an angle of ? = 5.20 degree with the vertical. How long are the strings?Explanation / Answer
mass of each sphere m = 0.19 g
charge on each sphere q = 7 n C = 7*10-9 C
? = 5.20 degrees
The sphere is in equillibrium under the application of force T from the string , the electric force From the other spring and gravitational force
Fx = T sin? - F = 0
F = T sin ? ......(1)
Fy = T cos? - mg = 0
T cos? = mg ......(2)
From equations (1) and (2)
tan? = F / mg
F = mg tan ?
using geometry of rightangle triangle
sin ? = a / L
a = L sin ?
Force between two charges is
F = k q 2 / r 2
mg tan ? = ( 9*109)(7*10-9 C)^2 / ( 2a)^2
( 0.19*10-3 kg ) ( 9.8 )tan ( 5.2) = ( 9*109)(7*10-9 C)^2 / ( 2a)^2
a = 0.0255
L sin ? = 0.0255
L = 0.281m
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