Two identical small metallic spheres, each of mass 0.20g, are suspended by pendu

Question

Two identical small metallic spheres, each of mass 0.20g, are suspended by pendulums by light strings, each measuring 30.0 cm, from a common point. The spheres are given the same electric charge, mand it is found that the two come to equilibrium when each string is at an angle of 5.0 degrees with the vertical. Which of the following statements is false?

a. If the length of the strings is increased, the angle of separation decreases. b. If the charge of the spheres is increased, the angle of separation decreases. c. If the mass of spheres is increased, the angle of separation decreases. d. If the ratio of charge of the spheres to the length of the strings is kept constant, the angle of separation remains constant.

Explanation / Answer

Two opposite charges will attract each other as well as pushed apart by electric field present.

Thus at the equilibrium there are two forces acting on each of the charge.

Take negative charge -q which is right side,

F1 is the force due to electric field and F2 is force due to charge +q

at the equilibrium,

F1 = F2

qE = kq^2/r^2

qE = kq^2/(Lsin)^2

qE = kq^2/[L^2sin^2()]

sin^2() = E/L^2kq

sin() = sqrt[E/L^2kq]

Above equation shows is directly proportional to E and inversely proportional to L and q and not depend on the mass.

Thus statement c) If the mass of spheres is increased, the angle of separation decreases is False.

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