$A$ simple pendulum of length $l$ has a brass bob attached at its lower end. Its period is $T$. If a steel bob of the same size,having a density $x$ times that of brass,replaces the brass bob and its length is changed so that the period becomes $2T$,then the new length is:

$A$ hollow sphere is filled with water through a small hole in it. It is then hung by a long thread and made to oscillate. As the water slowly flows out of the hole at the bottom, the period of oscillation will

The height of a swing changes during its motion from $0.1\, m$ to $2.5\, m$. The minimum velocity of a boy who swings in this swing is ..... $m/s$.

In a seconds pendulum,the mass of the bob is $30\, g$. If it is replaced by a $90\, g$ mass,then its time period will be .... $s$.

The bob of a pendulum of mass $m$, suspended by an inextensible string of length $L$ as shown in the figure, carries a small charge $q$. An infinite horizontal plane conductor with uniform surface charge density $\sigma$ is placed below it. What will be the time period of the pendulum for small amplitude oscillations?

The acceleration due to gravity at a place is $\pi^2 \, m/s^2$. Then the time period of a simple pendulum of length $1 \, m$ is: