The length of the seconds pendulum is $1 \,m$ on Earth. If the mass and diameter of a planet are $1.5$ times that of the Earth, the length of the seconds pendulum on the planet will be nearly (in $\,m$)

Two simple pendulums $A$ and $B$ are made to oscillate simultaneously. It is found that $A$ completes $10$ oscillations in $20 \ s$ and $B$ completes $8$ oscillations in $10 \ s$. The ratio of the lengths of $A$ and $B$ is

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 .... $cm$.

$A$ heavy small-sized sphere is suspended by a string of length $l$. The sphere rotates uniformly in a horizontal circle with the string making an angle $\theta$ with the vertical. Then the time period of this conical pendulum is

$A$ simple pendulum with an iron bob has a time period $T$. The bob is now immersed in a non-viscous liquid and oscillated. If the density of the liquid is $\frac{1}{12}$th that of iron,then the new time period will be:

$A$ simple pendulum with a bob of mass $m$ oscillates from $A$ to $C$ and back to $A$ such that $PB$ is $H$. If the acceleration due to gravity is $g$,then the velocity of the bob as it passes through $B$ is