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Question:

A simple pendulum of length L is placed between the plates of a parallel plate capacitor having electric field E, as shown in figure. Its bob has mass m and charge q. The time period of the pendulum is given by :

2π√L√(g²+(qEm)²)

2π√L√(g²−q²E²/m²)

2π√L(g−qEm)

2π√L(g+qEm)

Solution:

The effective acceleration due to gravity is given by:
geff = √(g² + (qE/m)²)
The time period of a simple pendulum is given by:
T = 2π√(L/geff)
Substituting the value of geff, we get:
T = 2π√(L/√(g² + (qE/m)²)) = 2π√[L√(g²+(qEm)²)]