The length of a seconds pendulum on the surface of the Earth is $1\, m$. The length of a seconds pendulum on the surface of the Moon,where $g$ is $1/6$th the value of $g$ on the surface of the Earth,is:

$A$ pendulum is executing simple harmonic motion and its maximum kinetic energy is $K_1$. If the length of the pendulum is doubled and it performs simple harmonic motion with the same angular amplitude as in the first case,its maximum kinetic energy is $K_2$,then:

$A$ pendulum is suspended by a string of length $250\,cm$. The mass of the bob of the pendulum is $200\,g$. The bob is pulled aside until the string is at $60^{\circ}$ with the vertical,as shown in the figure. After releasing the bob,the maximum velocity attained by the bob will be . . . . . . $m/s$. (if $g = 10\,m/s^2$)

$A$ simple pendulum hangs from the ceiling of a car. If the car accelerates with a uniform acceleration,the frequency of the simple pendulum will

$A$ simple pendulum of length $L$ has mass $M$ and it oscillates freely with amplitude $A$. At the extreme position,its potential energy is:

The bob of a simple pendulum of length $L$ is released from a position of small angular displacement $\theta$. Its linear displacement at time $t$ is ($g =$ acceleration due to gravity).