question_answer

A small sphere carrying a charge ?q? is hanging in between two parallel plates by a string of length L. Time period of pendulum is \[{{T}_{0}}\]. When parallel plates are charged, the time period changes to \[T\]. The ratio \[T/{{T}_{0}}\] is equal to [UPSEAT 2003]

A)            \[{{\left( \frac{g+\frac{qE}{m}}{g} \right)}^{1/2}}\]

B)                                      \[{{\left( \frac{g}{g+\frac{qE}{m}} \right)}^{3/2}}\]

C)            \[{{\left( \frac{g}{g+\frac{qE}{m}} \right)}^{1/2}}\]

D)            None of these

Correct Answer: C

Solution :

   Net downward force \[mg'=mg+QE\] Þ Effect acceleration \[g'=\left( g+\frac{QE}{m} \right)\] Hence time period  \[T=2\pi \sqrt{\frac{l}{g'}}=2\pi \sqrt{\frac{l}{\left( g+\frac{QE}{m} \right)}}\]