Question

A positively charged pendulum is oscillating in a uniform electric field pointing upward. Its time period as compared to that when it oscillates without electric field

Answer 1

Time period is given by $\bold{T=2\pi\sqrt{\frac{L}{a_{eff}}}}$
Here aeff is effective acceleration act on pendulum.

Case 1 :- without electric field.
without electric field intensity , only acceleration due to gravity acts on pendulum . So, effective acceleration ,aeff = g
∴ T = 2π√(L/g) -----(1)

Case2 :- with electric field
electric field acts on a positive charged pendulum and it is directed upward direction. ∴ Electrostatic force acts on pendulum is upward direction. So, Electrostatic acceleration acts on pendulum is upward direction.
∴ effective acceleration , aeff = g - qE/m [ here q is charged on pendulum of mass m and E is Electric field ]
Now, T' = 2π√(L/(g - qE/m) -----(2)

Now, time period with Electric field/time period without electric field = T'/T
= √(L/g)/√{L/(g - qE/m)}
= √{(g - qE/m)/g}

Hence, answer is √(g - qE/m) : √g

Answer 2

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