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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 a charge q. The pendulum Is placed in a uniform electric fleld of strength E directed vertically upwards.With what perlod will the pendulum oscillate if the electrostatic force acting on the sphere is less than the gravitational force? |
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Answer» Solution :Let the pendulum be at an angle of `theta` with the vertical. Net force acting on the bob =mg-qE Torque experienced by the bob about the POINT of suspension, `tau=-(mg-qE)lsintheta` (where, the negative sign indicates that the torque experienced is restoring torque) As the AMPLITUDE of oscillation is small,  `sintheta~~theta` Then, `tau=-(mg-qE)ltheta` again, `tau=` moment of inertia (l) `XX` angular acceleration `(ALPHA)` `thereforealpha=(tau)/I=(-(mg-qE)ltheta)/I=(-(mg-qE)ltheta)/(ml^(2))[becauseI=ml^(2)]` `=((-(g-(qE)/m)theta)/l` `thereforealphaprop-theta[because((g-(qE)/m))/l=`constant`]` `therefore` The pendulum executes an SHM. `therefore` Time period of the pendulum, `T=2pisqrt(("angular DISPLACEMENT")/("angular acceleration"))=2pisqrt((theta)/(alpha))` `thereforeT=2pisqrt(l/(g-(qE)/m))` |
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