The ratio of frequencies of two pendulums is $2 : 3$. What is the ratio of their lengths?

$A$ 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 acceleration due to gravity on the surface of the moon is $1.7 \; m s^{-2}$. What is the time period of a simple pendulum on the surface of the moon if its time period (in $s$) on the surface of the earth is $3.5 \; s$? ($g$ on the surface of the earth is $9.8 \; m s^{-2}$)

The bob of a simple pendulum of length $L$ has a mass $m$ and charge $q$. The pendulum is suspended between the plates of a charged parallel plate capacitor. The direction of the electric field is shown in the figure. The period of oscillations of the simple pendulum is (acceleration due to gravity $g > qE/m$):

The length of the simple pendulum is made $3$ times the original length. If $T$ is its original time period,then the new time period will be:

The period of oscillation of a simple pendulum of length $L$ suspended from the roof of a vehicle which moves without friction down an inclined plane of inclination $\alpha$,is given by