question_answer

A pendulum bob of mass m carrying a charge q is at rest with its string making an angle 9 with the vertical in a uniform horizontal electric field E, The tension in the string is

A)  \[\frac{mg}{\sin \theta }\] and \[\frac{qE}{\cos \theta }\]

B)  \[\frac{mg}{\cos \theta }\] and \[\frac{qE}{\sin \theta }\]

C)  \[\frac{qE}{mg}\]

D)  \[\frac{mg}{qE}\]

Correct Answer: B

Solution :

A pendulum bob of weight mg and carrying a charge q is suspended in the electric field E. Suppose that it comes to rest at point A, so that it makes an angle \[\theta \] with the vertical as shown. At point A, the bob is acted upon by the following three forces. (i) Weight mg acting vertically downward, (ii) Tension T in the string along AS (iii) Electrostatic force \[qE\] on the bob along horizontal. Since, the bob is in equilibrium under the action of the forces mg, T and \[qE\], these forces can be represented by the sides SN, AS and NA of triangle ANS. Therefore, \[\frac{mg}{SN}=\frac{qE}{NA}=\frac{T}{AS}\] \[\Rightarrow \] \[qE=T\,\sin \theta \] and \[mg=T\,\cos \theta \]