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

Frequency $f$ of a simple pendulum depends on its length $\ell$ and acceleration $g$ due to gravity according to the following equation $f = \frac{1}{2 \pi} \sqrt{\frac{g}{\ell}}$. $A$ graph between which of the following quantities is a straight line?

$A$ hollow pendulum bob filled with water has a small hole at the bottom through which water escapes at a constant rate. Which of the following statements describes the variation of the time period $T$ of the pendulum as the water flows out?

$A$ 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).

Using a simple pendulum experiment,$g$ is determined by measuring its time period $T$. Which of the following plots represents the correct relation between the pendulum length $L$ and time period $T$?

An object of mass $3 \,kg$ is tied by a string of negligible mass to a ceiling and held such that the string is taut. The object is released suddenly such that the string remains taut. Its acceleration when released is (acceleration due to gravity $= 10 \,ms^{-2}$) (in $\,ms^{-2}$)