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 ..... $m/s$.

Two pendulums of length $1.21 \,m$ and $1.0 \,m$ start vibrating. At some instant,the two are in the mean position in the same phase. After how many vibrations of the longer pendulum will the two be in phase again?

The ratio of frequencies of two pendulums is $2 : 3$. What is the ratio of their lengths?

In an experiment to determine the period of a simple pendulum of length $1\, m$,it is attached to different spherical bobs of radii $r_1$ and $r_2$. The two spherical bobs have uniform mass distribution. If the relative difference in the periods is found to be $5 \times 10^{-4}$,the difference in radii,$|r_1 - r_2|$,is best given by .... $cm$.

$A$ pendulum clock is running fast. To correct its time,we should

$A$ 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