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STD 12 - 2. Electric potential and capacitance — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 2. Electric potential and capacitance4 Marks
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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