If the mass of the bob in a simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is $\frac{x}{2}$ times its original time period. Then the value of $x$ is:

Two simple pendulum whose lengths are $1\,m$ 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 pendulum bob has a speed of $3\, {m} / {s}$ at its lowest position. The pendulum is $50 \,{cm}$ long. The speed of bob, when the length makes an angle of $60^{\circ}$ to the vertical will be $ …….\,{m} / {s}$ $\left(g=10 \,{m} / {s}^{2}\right)$

A simple pendulum is vibrating in an evacuated chamber, it will oscillate with

A solid cylinder of density $\rho_0$, cross-section area $A$ and length $l$ floats in a liquid of density $\rho\left( >\rho_0\right)$ with its axis vertical, as shown. If it is slightly displaced downward and released, the time period will be …….