A small sphere carrying a charge ‘q’ is hanging in between two pa… - Vidyadip

MCQ

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

A
${\left( {\frac{{g + \frac{{qE}}{m}}}{g}} \right)^{1/2}}$
B
${\left( {\frac{g}{{g + \frac{{qE}}{m}}}} \right)^{3/2}}$
✓
${\left( {\frac{g}{{g + \frac{{qE}}{m}}}} \right)^{1/2}}$
D
None of these

✓

Answer

Correct option: C.

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

c
(c) Net downward force $mg' = mg + QE$
$==>$ 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)}}} $

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