$A$ simple pendulum has a time period $T$ in air. Its time period when it is completely immersed in a liquid of density one-eighth the density of the material of the bob is:

The bob of a pendulum of mass $m$, suspended by an inextensible string of length $L$ as shown in the figure, carries a small charge $q$. An infinite horizontal plane conductor with uniform surface charge density $\sigma$ is placed below it. What will be the time period of the pendulum for small amplitude oscillations?

$A$ 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 $= 10^3\, kg/m^3$).

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?

$A$ child is sitting on a swing which performs $S.H.M$. It has minimum and maximum heights from the ground of $0.75 \,m$ and $2 \,m$ respectively. Its maximum speed will be $\left[g=10 \,m/s^2\right]$

An object of mass $3 \,kg$ is tied by a string of negligible mass to a ceiling and held such that the string is taut. The object is released suddenly such that the string remains taut. Its acceleration when released is (acceleration due to gravity $= 10 \,ms^{-2}$) (in $\,ms^{-2}$)