Question
A pendulum bob of mass $$m$$ carrying a charge $$q$$ is at rest with its string making an angle $$\theta $$ with the vertical in a uniform horizontal electric field $$E.$$ The tension in the string is
A.
$$\frac{{mg}}{{\sin \theta }}\,{\text{and}}\,\frac{{qE}}{{\cos \theta }}$$
B.
$$\frac{{mg}}{{\cos \theta }}\,{\text{and}}\,\frac{{qE}}{{\sin \theta }}$$
C.
$$\frac{{qE}}{{mg}}$$
D.
$$\frac{{mg}}{{qE}}$$
Answer :
$$\frac{{mg}}{{\cos \theta }}\,{\text{and}}\,\frac{{qE}}{{\sin \theta }}$$
Solution :
In equilibrium,
$$\eqalign{ & T\cos \theta = mg\,.......\left( 1 \right) \cr & T\sin \theta = qE\,.......\left( 2 \right) \cr} $$
From (1), $$T = \frac{{mg}}{{\cos \theta }}$$
From (2), $$T = \frac{{qE}}{{\sin \theta }}$$
In equilibrium,
$$\eqalign{ & T\cos \theta = mg\,.......\left( 1 \right) \cr & T\sin \theta = qE\,.......\left( 2 \right) \cr} $$
From (1), $$T = \frac{{mg}}{{\cos \theta }}$$
From (2), $$T = \frac{{qE}}{{\sin \theta }}$$
