The time period of a simple pendulum is $4 \ s$ at a place on the Earth where the acceleration due to gravity is $\pi^2 \ ms^{-2}$. The length of the pendulum in meters is:

$A$ block of mass $m$ is sliding on a fixed frictionless concave surface of radius $R$. It is released from rest at point $P$ which is at a height of $H \ll R$ from the lowest point $Q$.
$(a)$ What is the potential energy as a function of $\theta$,taking the lowest point $Q$ as the reference level for potential energy?
$(b)$ What is the kinetic energy as a function of $\theta$?
$(c)$ What is the time taken for the particle to reach from point $P$ to the lowest point $Q$?
$(d)$ How much force is exerted by the block on the concave surface at the point $Q$?

$A$ simple pendulum of period $T$ has a metal bob which is negatively charged. If it is allowed to oscillate above a positively charged metal plate,its period will

$A$ cuboidal piece of wood has dimensions $a, b$ and $c$. Its relative density is $d$. It is floating in a large body of water such that side $a$ is vertical. It is pushed down a bit and released. The time period of $SHM$ executed by it is:

$A$ simple pendulum of length $L$ swings in a vertical plane. The tension in the string when it makes an angle $\theta$ with the vertical and the bob of mass $m$ moves with a speed $v$ is (where $g$ is the gravitational acceleration):

If a simple pendulum can reach a height of $10 \ cm$,what is its velocity when it is at its mean position (in $m/s$)? $(g = 9.8 \ m/s^2)$