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

$A$ body of mass $2 \, kg$ is tied to a string of length $2 \, m$ and rotated in a vertical circle. What is the difference between the maximum and minimum kinetic energy in $J$?

$A$ particle with charge $Q$ coulomb, tied at the end of an inextensible string of length $R$ metre, revolves in a vertical plane. At the centre of the circular trajectory, there is a fixed charge of magnitude $Q$ coulomb. The mass of the moving charge $M$ is such that $Mg = \frac{Q^2}{4 \pi \epsilon_0 R^2}$. If at the highest position of the particle, the tension of the string just vanishes, the horizontal velocity at the lowest point has to be

$A$ fighter plane is moving in a vertical circle of radius $r$. Its minimum velocity at the highest point of the circle will be

$A$ particle originally at rest at the highest point of a smooth vertical circle (radius $R = 1.8 \ m$) is slightly displaced. It will leave the circle at a vertical distance $h$ from the bottom. The value of $h$ will be ..... $m$.

$A$ stone of mass $150 \ g$ moves in a vertical circle at the end of a string. The radius of the circle is $70 \ cm$ and the speed of the stone at the topmost point $P$ is $3.5 \ m/s$. For the instant at which the stone passes through the highest point $P$,the centripetal force is nearly ......... $N$ (take $g = 10 \ m/s^2$).