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Two small metallic spheres, each of mass m = 0.184 g, are suspended as pendulums

ID: 2125810 • Letter: T

Question

Two small metallic spheres, each of mass m = 0.184 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 7.7 nC, and they come to equilibrium when each string is at an angle of ?= 4.70

Two small metallic spheres, each of mass m = 0.184 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 7.7 nC, and they come to equilibrium when each string is at an angle of ?= 4.70 degree with the vertical.

Explanation / Answer

mass of each sphere m = 0.184 g

charge on each sphere q = 7. n C = 7.7*10-9 C

? = 4.70 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)(7.7*10-9 C)2 / ( 2a)2

( 0.184*10-3 kg ) ( 9.8 )tan ( 4.7) = ( 9*109)(7.7*10-9 C)2 / ( 2a)2

a = 0.0298

L sin ? = 0.0298

L = 0.364m

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