$A$ 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).

$A$ bob of a simple pendulum of mass $m$ is displaced through $90^{\circ}$ from the mean position and released. When the bob is at the lowest position,the tension in the string is:

Given below are two statements:
Statement $I :$ $A$ second's pendulum has a time period of $1$ second.
Statement $II :$ It takes precisely one second to move between the two extreme positions.
In the light of the above statements,choose the correct answer from the options given below:

The ratio of the period of oscillation of a conical pendulum to that of a simple pendulum is: (Assume the strings are of the same length in both cases and $\theta$ is the angle made by the string with the vertical in the case of the conical pendulum.)

The period of oscillation of a simple pendulum of length $L$ suspended from the roof of a vehicle which moves without friction down an inclined plane of inclination $\alpha$,is given by

$A$ simple pendulum,suspended from the ceiling of a stationary van,has time period $T$. If the van starts moving with a uniform velocity,the period of the pendulum will be