$A$ simple pendulum is hanging from the ceiling of a lift. When the lift is at rest,the time period of the pendulum is $T$. If the resultant acceleration becomes $g/4$,then the new time period of the pendulum is: (in $, T$)

$A$ simple pendulum of length $l$ and mass $m$ of the bob is suspended in a car that is travelling with a constant speed $v$ around a circular path of radius $R$. If the pendulum undergoes oscillations with small amplitude about its equilibrium position,the frequency of its oscillations will be

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

Two pendulums begin to swing simultaneously. If the ratio of the frequency of oscillations of the two is $7 : 8$,then the ratio of lengths of the two pendulums will be

The breaking strength of the string of a simple pendulum is twice the weight of the bob. The bob is released from rest when the string is horizontal. At what angle $\theta$ with the vertical will the string break?

The ratio of the frequencies of two simple pendulums is $4: 3$ at the same place. The ratio of their respective lengths is