The period of a simple pendulum,whose bob is a hollow metallic sphere,is $T$. The period is $T_1$ when the bob is filled with sand,$T_2$ when it is filled with mercury and $T_3$ when it is half filled with mercury. Which of the following is true?

$A$ bob of mass $m$ suspended by a thread of length $l$ undergoes simple harmonic oscillations with time period $T$. If the bob is immersed in a liquid that has density $1/4$ times that of the bob and the length of the thread is increased by $1/3$ of the original length,then the time period of the simple harmonic oscillations will be :-

$A$ pendulum suspended from the ceiling of a train has a period $T$ when the train is at rest. When the train travels the same distance per unit time,the period of oscillation is

$A$ cylindrical block of wood (density $= 650 \ kg \ m^{-3}$),of base area $30 \ cm^2$ and height $54 \ cm$,floats in a liquid of density $900 \ kg \ m^{-3}$. The block is depressed slightly and then released. The time period of the resulting oscillations of the block would be equal to that of a simple pendulum of length ..... $cm$ (nearly).

$A$ simple pendulum consists of a small sphere of mass $m$ suspended by a thread of length $l$. The sphere carries a positive charge $q$. The pendulum is allowed to do small oscillations in a uniform electric field $E$ with direction vertically upwards. The time period of oscillation is

The bob of a simple pendulum is a spherical hollow ball filled with water. $A$ plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During observation,till water is coming out,the time period of oscillation would: