The bob of a simple pendulum is of mass $10 \, g$. It is suspended with a thread of $1 \, m$. If we hold the bob so as to stretch the string horizontally and release it,what will be the tension at the lowest position? (Take $g = 10 \, m/s^2$)

$A$ body of mass $m \ kg$ is rotating in a vertical circle at the end of a string of length $r \ m$. What is the difference in the kinetic energy at the top and the bottom of the circle?

$A$ body of mass $m$ is suspended from a string of length $l$. What is the minimum horizontal velocity that should be given to the body in its lowest position so that it may complete one full revolution in a vertical plane with the point of suspension as the center of the circle?

$A$ heavy mass is attached at one end of a thin wire and whirled in a vertical circle. The chances of breaking the wire are maximum when:

$A$ small body slides down a smooth uneven surface from a height $H$,which eventually emerges into a circular loop of radius $R (< H)$. What should be the value of $H$,so that the force on the body at $A$ is $\sqrt{2}$ times its weight?

$A$ particle of mass $m$ is tied to one end of a string of length $l$. The particle is held horizontal with the string 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