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A simple pendulum consists of a small sphere of mass m suspended by a thread of length l. The sphere carries apositive charge q. Thependulum is placed in a uniform electric field of strength E directed vertically downwards. Finds the period of oscillation of the pendulum due to the electrostatic force acting on the sphere, neglecting the effect of the gravitational force. |
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Answer» Solution :Let the pendulum be be displaced from its equilibrium position A to position B through a small angle ` THETA ` and then released. Forces acting on pendulum are (i)force F= qEin vertical DOWNWARD direction DUE to the electrical field, and (ii ) the tension `T_0` and hence unbalanced restoring forceis qE `SIN theta` if ` theta ` is small then ` sin theta =theta =(arc AB)/(1) ` ` therefore `Restoring force `=-qE theta =(-qE)/(l) (areAB)` obviously the MOTION of pendulum is SHM ,whose time period is given as: `T=2pi sqrt(("inertia factor ")/("spring factor ") )=2pi sqrt((m)/(qE//l))=2pi sqrt((ml)/(qE))` ` (##U_LIK_SP_PHY_XII_C01_E09_020_S01.png" width="80%"> |
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