$A$ simple pendulum with length $100\,cm$ and bob of mass $250\,g$ is executing $S$.$H$.$M$. of amplitude $10\,cm$. The maximum tension in the string is found to be $\frac{x}{40}\,N$. The value of $x$ is $..........$.

$A$ string of a pendulum of length $l$ is displaced through $90^{\circ}$ from its vertical and released. Then,the minimum strength of the string needed to withstand the tension as the pendulum passes through its mean position is

$A$ simple pendulum is taken to a place where its distance from the Earth's surface is equal to the radius of the Earth. Calculate the time period of small oscillations if the length of the string is $4.0 \ m$. (Take $g = \pi^2 \ m/s^2$ at the surface of the Earth.) (in $s$)

$A$ pendulum is suspended by a string of length $250\,cm$. The mass of the bob of the pendulum is $200\,g$. The bob is pulled aside until the string is at $60^{\circ}$ with the vertical,as shown in the figure. After releasing the bob,the maximum velocity attained by the bob will be . . . . . . $m/s$. (if $g = 10\,m/s^2$)

$A$ simple pendulum of period $T$ has a metal bob which is negatively charged. If it is allowed to oscillate above a positively charged metal plate,its period will

The time period of a simple pendulum in a stationary lift is $T$. If the lift accelerates with $\frac{g}{6}$ vertically upwards,then the new time period will be:
(where $g =$ acceleration due to gravity)