First slide

Electric field

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 T₀. when parallel plates are charged, the time period changes to T. The ratio T/T₀ is equal to

Moderate

A

${(\frac{g + \frac{q E}{m}}{g})}^{1 / 2}$
B

${(\frac{g}{g + \frac{q E}{m}})}^{3 / 2}$
C

${(\frac{g}{g + \frac{q E}{m}})}^{1 / 2}$
D

none of these

Solution

Net downward force $m g^{'} = m g + q E$
$\Rightarrow Effect acceleration g^{'} = (g + \frac{q E}{m})$
Hence time period
$\begin{array}{l} T = 2 π \sqrt{\frac{l}{g^{'}}} = 2 π \cdot \sqrt{\frac{l}{(g + \frac{q E}{m})}} \\ G i v e n : T_{0} = 2 π \sqrt{\frac{l}{g}} \\ So, \frac{T}{T_{0}} = \sqrt{\frac{g}{g + \frac{q E}{m}}} \end{array}$

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