The acceleration due to gravity at a place is $\pi^2 \, m/s^2$. Then the time period of a simple pendulum of length $1 \, m$ is:

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?

To show that a simple pendulum executes simple harmonic motion,it is necessary to assume that

$A$ pendulum bob has a speed of $3\, m/s$ at its lowest position. The pendulum is $0.5\, m$ long. The speed of the bob,when the length makes an angle of $60^o$ with the vertical,will be ..... $m/s$ (If $g = 10\, m/s^2$)

Identify the correct statement.

The ratio of the frequencies of two simple pendulums is $4: 3$ at the same place. The ratio of their respective lengths is