If a simple pendulum is taken to a place where $g$ decreases by $2\%$,then the time period:

$A$ simple pendulum is suspended from the roof of a trolley which moves in a horizontal direction with an acceleration $a$. The time period is given by $T = 2\pi \sqrt{\frac{l}{g'}}$,where $g'$ is equal to:

Savitha, a $XI$ standard student, while conducting an experiment to determine the effective length of a simple pendulum $L$, notes down the data of time taken to complete $30$ oscillations as $60 \text{ s}$ and hence calculates the length of the simple pendulum as: (Take $\pi^2 = 9.8$, and $g = 9.8 \text{ m/s}^2$) (in $\text{ m}$)

The time period of a simple pendulum is $T$. If its length is increased by $21\%$,what is the percentage increase in its time period?

$A$ simple pendulum is hanging from a peg inserted in a vertical wall. Its bob is stretched in a horizontal position from the wall and is left free to move. The bob hits the wall,and the coefficient of restitution is $\frac{2}{\sqrt{5}}$. After how many collisions will the amplitude of vibration become less than $60^\circ$?

$A$ 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).