A) \[\frac{\text{mg}}{\text{sin}}\text{and}\frac{\text{qE}}{\text{cos}\,}\]
B) \[\frac{\text{mg}}{\text{cos}}\text{and}\frac{\text{qE}}{\sin \,}\]
C) \[\frac{\text{qE}}{mg}\]
D) \[\frac{mg}{\text{qE}}\]
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. Therefor, \[\frac{mg}{SN}=\frac{qE}{NA}=\frac{T}{AS}\] \[\Rightarrow \] \[qE=T\sin \theta \] and \[mg=T=\cos \theta \]You need to login to perform this action.
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