$A$ stone of mass $40$ g is tied to a light inextensible string of length $50$ cm and whirled in a vertical circle at the rate of $30$ revolutions per minute. The tension in the string when it is at the lowest point of the circle is (Take gravitational acceleration, $g = 10 \text{ m/s}^2$ and $\pi^2 = 10$) (in $N$)

$A$ 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. If $\theta$ is the instantaneous angle which the line joining the particle and the centre of the loop makes with the vertical,then identify the correct statement$(s)$ related to the normal reaction $N$ between the block and the surface.

$A$ body of mass $m$ is tied to a string of length $l$ and rotated in a vertical circle. What is the difference in tension between the lowest point and the highest point (in $,mg$)?

$A$ particle is whirled in a vertical circle of radius $1.0 \ m$ using a string with one end fixed. If the ratio of maximum and minimum tension in the string is $\frac{5}{3}$,the minimum velocity of the particle during circular motion is ......... $ms^{-1}$.

$A$ mass $m$ is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when

$A$ 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: