A particle of mass $m$ is tied to one end of $a$ string of length $l$. The particle is held horizontal with the string $mg$ taut. It is then projected upward with $a$ velocity $u$. The tension in the string is $\frac{{mg}}{2}$ when it is inclined at an angle $30^o$ to the horizontal. The value of $u$ is

A body of mass $1\,kg$ is rotating in a vertical circle of radius $1\,m$. What will be the difference in its kinetic energy at the top and bottom of the circle : ………… $\mathrm{J}$ $(g = 10\,m/s^2)$

A $2\, kg$ stone at the end of a string $1\, m$ long is whirled in a vertical circle at a constant speed. The speed of the stone is $4\, ms^{-1}$. The tension in the string will be $52\, N$ when the stone is

A pendulum bob on a $2\, m$ string is displaced $60^{°}$ from the vertical and then released. What is the speed of the bob as it passes through the lowest point in its path ………. $m/s$

The string of pendulum of length $l$ is displaced through ${90^o}$ from the vertical and released. Then the minimum strength of the string in order to withstand the tension, as the pendulum passes through the mean position is