$A$ bucket filled with water is tied to a string of length $1.6 \, m$ and rotated in a vertical circle. What should be the minimum velocity at the highest point so that the water does not spill? $(g = 10 \, m/s^2)$

$A$ weightless string can support a tension up to $30 \,N$. $A$ stone of mass $0.5 \,kg$ is tied to its one end and is revolved in a circular path of radius $2 \,m$ in a vertical plane. Then the maximum angular velocity of the stone will be (acceleration due to gravity $g=10 \,m/s^2$)

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

$A$ bucket filled with water is revolved in a vertical circle of radius $4 \ m$ and the water just does not fall down. The time period of revolution will be ........ $s$.

$A$ 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)

$A$ 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 ..... $m$.