$A$ simple pendulum of string length $30 \ cm$ performs $20$ oscillations in $10 \ s$. The length of the string required for the pendulum to perform $40$ oscillations in the same time duration is . . . . . . $cm$. [Assume that the mass of the pendulum remains same.]

$A$ pendulum is suspended by a string of length $250\,cm$. The mass of the bob of the pendulum is $200\,g$. The bob is pulled aside until the string is at $60^{\circ}$ with the vertical,as shown in the figure. After releasing the bob,the maximum velocity attained by the bob will be . . . . . . $m/s$. (if $g = 10\,m/s^2$)

$A$ simple pendulum is suspended in a lift which is going up with an acceleration $5 \ m/s^2$. An electric field of magnitude $5 \ N/C$ and directed vertically upward is also present in the lift. The charge of the bob is $1 \ mC$ and mass is $1 \ mg$. Taking $g = \pi^2 \ m/s^2$ and length of the simple pendulum $1 \ m$,the time period of the simple pendulum is ...... $s$.

$A$ simple pendulum, consisting of a small ball of mass $m$ attached to a massless string hanging vertically from the ceiling, is oscillating with an amplitude such that $T_{\max } = 2 T_{\min }$, where $T_{\max }$ and $T_{\min }$ are the maximum and minimum tension in the string respectively. The value of maximum tension $T_{\max }$ in the string is

$A$ wooden cube (density of wood $d$) of side $l$ floats in a liquid of density $\rho$ with its upper and lower surfaces horizontal. If the cube is pushed slightly down and released,it performs simple harmonic motion of period $T$. Then,$T$ is equal to

If the length of an oscillating simple pendulum is made $\frac{1}{3}$ times at a place while keeping the amplitude the same,then its total energy $(E)$ will be: (in $E$)