$A$ particle of mass $m$ is tied to a string of length $l$ and whirled in a vertical circle. The difference in tension and kinetic energy at the highest and lowest positions of the circular path will be:

$A$ bucket tied at the end of a $1.6\, m$ long string is whirled in a vertical circle with constant speed. What should be the minimum speed so that the water from the bucket does not spill,when the bucket is at the highest position? (Take $g = 10\, m/s^2$)

$A$ small bob tied at one end of a thin string of length $1\, m$ is describing a vertical circle so that the maximum and minimum tension in the string are in the ratio $5: 1$. The velocity of the bob at the highest position is ............. $m/s$ (Take $g=10\, m/s^2$).

What is the minimum velocity with which a body of mass $m$ must enter a vertical loop of radius $R$ so that it can complete the loop $?$

$A$ stone of mass $1 \ kg$ tied to a light inextensible string of length $L = \frac{5}{3} \ m$ is rotating in a circular path of radius $L$ in a vertical plane. If the ratio of maximum tension in the string to the minimum tension in the string is $3$,the speed of the stone at the highest point of the circle is ($g =$ acceleration due to gravity).

$A$ light rigid wire of length $1 \,m$ is attached to a ball of mass $500 \,g$ at one end. The other end of the wire is fixed, so that the wire can rotate freely in the vertical plane about its fixed end. At the lowest point of the circular motion, the ball is given a horizontal velocity of $6 \,m/s$. Determine the radial component of the acceleration of the ball when this rigid wire makes an angle of $60^{\circ}$ with the upward vertical. (Take $g = 10 \,m/s^2$) (in $\,m/s^2$)