If the length of the pendulum in a pendulum clock increases by $0.1\, \%$,then the error in time per day is: (in $s$)

$A$ simple pendulum oscillates in a vertical plane. When it passes through the mean position,the tension in the string is $3$ times the weight of the pendulum bob. What is the maximum displacement of the pendulum string with respect to the vertical in degrees?

Using a simple pendulum experiment, $g$ is determined by measuring its time period $T$. Which of the following plots represents the correct relation between the pendulum length $L$ and time period $T$?

$A$ simple pendulum consisting of a mass $M$ attached to a string of length $L$ is released from rest at an angle $\alpha$. $A$ pin is located at a distance $l$ below the pivot point. When the pendulum swings down,the string hits the pin as shown in the figure. The maximum angle $\theta$ which the string makes with the vertical after hitting the pin is:

$A$ cylindrical plastic bottle of negligible mass is filled with $310\, ml$ of water and left floating in a pond with still water. If pressed downward slightly and released,it starts performing simple harmonic motion at angular frequency $\omega$. If the radius of the bottle is $2.5\, cm$,then $\omega$ is close to ..... $rad\, s^{-1}$ (density of water $= 10^3\, kg/m^3$).

$A$ simple pendulum with an iron bob has a time period $T$. The bob is now immersed in a non-viscous liquid and oscillated. If the density of the liquid is $\frac{1}{12}$th that of iron,then the new time period will be: