Question

Two identical small metallic spheres, each of mass .20 g, are suspended by pendulums by light strings from a common point. The spheres are given the same electric charge, and it is found that the two come to equilibrium when each string is at an angle of 5 degrees with the vertical. If each string is 30.0 cm long, which statement is false?

A) If the mass of the spheres is increased the angle of separation decreases.

B) If the ratio of charge of the spheres to length of the string is kept constant, the angle of separation remains constant.

C) If the length of the strings is increased, the angle of separation decreases.

D) If the charge of spheres is increased the angle of separation decreases.

Answer 1

At the equilibrium,

Fleft = Fright

null

kq^2/d^2 = qE =

kq^2/(Lsinθ)^2 = qE

kq^2/[L^2sin^2(θ)] = qE

kq/[L^2sin^2(θ)] = E

sin^2(θ) = E/L^2kq

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

As a results , A) If the mass of the spheres is increased the angle of separation decreases.the statement is false.