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 $m \ s^{-1}$)

The time period of a simple pendulum is $T$. When the length is increased by $10 \ cm$, its period is $T_1$. When the length is decreased by $10 \ cm$, its period is $T_2$. Then, the relation between $T, T_1$, and $T_2$ is

$A$ hollow sphere is filled with water through a small hole in it. It is then hung by a long thread and made to oscillate. As the water slowly flows out of the hole at the bottom,the period of oscillation will

$A$ cylindrical cork of uniform density floats in a liquid of density $\rho_1$. If the cork is depressed slightly and released, it oscillates harmonically with time period $T$. If the same cork floats in another liquid of density $\rho_2$, then the similar oscillation has time period $2T$. The value of $\rho_2/\rho_1$ is :

If the length of a seconds pendulum becomes $\frac{1}{3}$ of its original length,what will be its new periodic time?

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: