$A$ second's pendulum is mounted in a rocket. Its period of oscillation decreases when the rocket

$A$ simple pendulum of length $L$ and mass (bob) $M$ is oscillating in a plane about a vertical line between angular limits $-\varphi$ and $+\varphi$. For an angular displacement $\theta$ $(|\theta| < \varphi)$,the tension in the string and the velocity of the bob are $T$ and $v$ respectively. Which of the following relations hold good under the above conditions?

Identify the correct statement.

$A$ string of a pendulum of length $l$ is displaced through $90^{\circ}$ from its vertical and released. Then,the minimum strength of the string needed to withstand the tension as the pendulum passes through its mean position is

Two simple pendulums whose lengths are $100 \ cm$ and $121 \ cm$ are suspended side by side. Their bobs are pulled together and then released. After how many minimum oscillations of the longer pendulum,will the two be in phase again?

The metallic bob of a simple pendulum has the relative density $\rho$. The time period of this pendulum is $T$. If the metallic bob is immersed in water,then the new time period is given by