Question

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 $\frac{T}{T_0}$ is equal to

• 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

Answer 1

The correct option is C ${\left(\frac{g}{g+\frac{qE}{m}}\right)}^{1/2}$


Net downward force $m{g}^{{}^{\prime }}=mg+QE$
$\Rightarrow$ Effect acceleration $g^{{}^{\prime }}=(g+\frac{QE}{m})$
Hence time period $T=2\pi \sqrt{\frac{1}{g^{{}^{\prime }}}}=2\pi \sqrt{\frac{1}{(g+\frac{QE}{m})}}$