$A$ simple pendulum,suspended from the ceiling of a lift,has a period of oscillation $T$,when the lift is at rest. If the lift starts moving upwards with an acceleration $a = 3g$,then the new period will be

$A$ 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.]

$A$ simple pendulum of length $l$ and having a bob of mass $M$ is suspended in a car. The car is moving on a circular track of radius $R$ with a uniform speed $v$. If the pendulum makes small oscillations in a radial direction about its equilibrium position,what will be its time period?

The time period of oscillations of a simple pendulum is $1$ minute. If its length is increased by $44 \%$,then its new time period of oscillation will be ......... $s$.

$A$ small sphere oscillates simple harmonically in a watch glass whose radius of curvature is $1.6 \ m$. The period of oscillation of the sphere is (acceleration due to gravity $g = 10 \ m/s^2$) (in $\pi \ s$)

$A$ simple pendulum with a bob of mass $40 \ g$ and charge $+2 \ \mu C$ makes $20$ oscillations in $44 \ s$. $A$ vertical electric field of magnitude $4.2 \times 10^4 \ NC^{-1}$ pointing downward is applied. The time taken by the pendulum to make $15$ oscillations in the electric field is (acceleration due to gravity $= 10 \ ms^{-2}$) (in $s$)