The time period of a simple pendulum,on a satellite orbiting the Earth,is

$A$ bob of a simple pendulum has mass $m$ and is oscillating with an amplitude $a$. If the length of the pendulum is $L$,then the maximum tension in the string is (given $\cos 0^{\circ}=1, g=$ acceleration due to gravity):

The bob of a simple pendulum performs $SHM$ with period $T$ in air and with period $T_1$ in water. The relation between $T$ and $T_1$ is (neglect friction due to water,density of the material of the bob is $\frac{9}{8} \times 10^3 \ kg/m^3$,density of water is $1 \ g/cc$):

$A$ pendulum is oscillating at a frequency of $8 \,Hz$. Suddenly, the string of the pendulum is clamped at its midpoint. What is the new frequency of oscillations (in $\,Hz$)?

If a simple pendulum is released from the given position,find the velocity of the bob when it reaches the lowest position. (Take $g = 10 \ m/s^2$) (in $m/s$)

$A$ cuboidal piece of wood has dimensions $a, b$ and $c$. Its relative density is $d$. It is floating in a large body of water such that side $a$ is vertical. It is pushed down a bit and released. The time period of $SHM$ executed by it is: