$A$ body of mass $0.4\, kg$ is whirled in a vertical circle making $2\, rev/sec$. If the radius of the circle is $2\, m$,then tension in the string when the body is at the top of the circle,is ......... $N$.

$A$ stone tied to a string of length $L$ is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed $u$. The magnitude of the change in its velocity as it reaches a position where the string is horizontal is

$A$ bucket containing water is revolved in a vertical circle of radius $r$. To prevent the water from falling down,the minimum frequency of revolution required is ($g =$ acceleration due to gravity).

$A$ particle of mass $m$ is released from a height $H$ on a smooth curved surface which ends into a vertical loop of radius $R$,as shown. Choose the correct alternative$(s)$ if $H = 2R$.

$A$ small cube with mass $M$ starts at rest at point $1$ at a height $4R$,where $R$ is the radius of the circular part of the track. The cube slides down the frictionless track and around the loop. The force that the track exerts on the cube at point $2$ is nearly ......... times the cube's weight $mg$.

$A$ bob of mass $m$ is suspended by a light string of length $L$. It is imparted a horizontal velocity $v_{o}$ at the lowest point $A$ such that it completes a circular trajectory in the vertical plane with the string becoming slack only on reaching the topmost point,$C$. This is shown in the figure. Obtain an expression for: $(i) v_{o}$; $(ii)$ the speeds at points $B$ and $C$; $(iii)$ the ratio of the kinetic energies $(K_{B} / K_{C})$ at $B$ and $C$. Comment on the nature of the trajectory of the bob after it reaches the point $C$.