A uniform rod of length $2.0 \,m$ is suspended through an end and is set into oscillation with small amplitude under gravity. The time period of oscillation is approximately .... $\sec$

A simple pendulum is executing simple harmonic motion with a time period $T$. If the length of the pendulum is increased by $21\%$, the percentage increase in the time period of the pendulum of increased length is ..... $\%$

The angular amplitude of a simple pendulum is $\theta_0$. The maximum tension in its string will be

Two pendulums begin to swing simultaneously. If the ratio of the frequency of oscillations of the two is $7 : 8$, then the ratio of lengths of the two pendulums will be

A simple pendulum of length $1\,m$ is allowed to oscillate with amplitude $2^o$. It collides elastically with a wall inclined at $1^o$ to the vertical. Its time period will be : (use $g = \pi ^2$ )

A simple pendulum has time period 't'. Its time period in a lift which is moving upwards with acceleration $3 ms ^{-2}$ is