$A$ pendulum has a time period $T$ in air. When it is made to oscillate in water, its time period is $\sqrt{2} T$. Then the relative density of the material of the bob of the pendulum is (neglect damping).

The bob of a simple pendulum of length $200 \ cm$ is released from a horizontal position. If $10 \%$ of its initial energy is lost due to air resistance,then the speed of the bob at the mean position is (Acceleration due to gravity $= 10 \ m \ s^{-2}$) (in $m \ s^{-1}$)

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

When a pendulum clock is running fast,what should be done to adjust it to the true time?

$A$ simple pendulum having length $\ell$ has a speed of $\sqrt{2g\ell}$ at the bottom-most point of its trajectory. Its motion will be:

The time period of a simple pendulum is $T$. The angular amplitude is $\beta$. How much time will the bob of the pendulum take to move from the equilibrium position $O$ to position $A$,where the string makes an angle $\alpha$ with the vertical?