$A$ pendulum of length $l = 1\,m$ is released from $\theta_0 = 60^\circ$. The rate of change of speed of the bob at $\theta = 30^\circ$ is ........ $m/s^2$ $(g = 10\,m/s^2)$.

Two pendulums begin to swing simultaneously. The first pendulum makes $11$ full oscillations when the other makes $9$. The ratio of the lengths of the two pendulums is

If the length of a clock pendulum increases by $0.2 \%$ due to atmospheric temperature rise,then the loss in time of the clock per day is ........... $s$.

$A$ simple pendulum of length '$l$' and a bob of mass '$m$' is executing $S$.$H$.$M$. of small amplitude '$A$'. The maximum tension in the string will be ($g=$ acceleration due to gravity).

Given below are two statements:
Statement $I :$ $A$ second's pendulum has a time period of $1$ second.
Statement $II :$ It takes precisely one second to move between the two extreme positions.
In the light of the above statements,choose the correct answer from the options given below:

$A$ seconds pendulum is placed in a space laboratory orbiting round the Earth at a height $3R$ from the Earth's surface. The time period of the pendulum will be ($R =$ radius of Earth).