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

$A$ 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):

The length of a simple pendulum is increased by $44\%$. The percentage increase in its time period will be ..... $\%$

The bob of a simple pendulum executes simple harmonic motion in water with a period $t$,while the period of oscillation of the bob is ${t_0}$ in air. Neglecting the frictional force of water and given that the density of the bob is $(4/3) \times 1000 \ kg/m^3$. What relationship between $t$ and ${t_0}$ is true?

What is the frequency of oscillation of a pendulum suspended in a freely falling lift?

$A$ small sphere oscillates simple harmonically in a watch glass whose radius of curvature is $1.6 \ m$. The period of oscillation of the sphere is (acceleration due to gravity $g = 10 \ m/s^2$) (in $\pi \ s$)