A simple pendulum of length $l$ has a bob of mass $m$ with a charge $q$ on it. A vertical sheet with surface charge density $\sigma$ passes through the point of suspension $O$. At equilibrium, the string makes an angle $\theta$ with the vertical, then -

Q. A simple pendulum of length $l$ and bob mass $m$ is hanging in front of a large non-conducting sheet having surface charge density $\sigma$. If suddenly a charge $+q$ is given to the bob & it is released from the position shown in figure. The maximum angle through which the string is deflected from vertical is $x{\tan }^{-1}\left(\frac{\sigma q_0}{2{\epsilon }_{0}mg}\right)$. Find $x$.

Q. A simple pendulum of length $l$ and mass (bob) $m$ is suspended vertically. The string makes an angle $\theta$ with the vertical. The restoring force acting on the pendulum is:

Q. A pendulum bob of mass $m$ carrying a charge $q$ is at rest with its string making an angle $\theta$ with the vertical in a uniform horizontal electric field $E$. The tension in the string is

Q. A nail is fixed at a point $P$ vertically below the point of suspension '$O$' of a simple pendulum of length $1m$. The bob is released when the string of pendulum makes an angle ${30}^0$ with horizontal. The bob reaches lowest point then describes vertical circle whose centre coincides with $P$. The least distance of $P$ from $O$ is:

Q. A simple pendulum with bob of mass m and length $l$ is held in position at an angle $\theta$ with the vertical. Its speed when it passes the lowest position is