The mass and diameter of a planet are twice those of Earth. What will be the period of oscillation of a pendulum on this planet if it is a seconds pendulum on Earth?

Two masses,both equal to $100\, g$,are suspended at the ends of identical light strings of length $\ell = 1.0\, m$,attached to the same point on the ceiling (see figure). At time $t = 0$,they are simultaneously released from rest,one at angle $\theta_1 = 1^o$,the other at angle $\theta_2 = 2^o$ from the vertical. The masses will collide

The time period of a simple pendulum is $T$. If its length is increased by $21\%$,what is the percentage increase in its time period?

$A$ coin is placed on a horizontal plate. The plate performs $S.H.M.$ vertically with an angular frequency $\omega$. The amplitude $A$ of oscillations is gradually increased. The coin will lose contact with the plate for the first time when the amplitude is ($g =$ acceleration due to gravity).

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?

$A$ pendulum oscillates simple harmonically if and only if:
$I$. The size of the bob of the pendulum is negligible in comparison with the length of the pendulum.
$II$. The angular amplitude is less than $10^{\circ}$.
Choose the correct option.