$A$ 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 $g = 10 \ m/s^2$).

$A$ stone tied to a string is rotated in a vertical circle. The minimum speed with which the string has to be rotated at the lowest point is:

$A$ stone of mass $m$ is moving in a vertical circle of radius $20 \ cm$. What is the difference in kinetic energy between the lowest and highest points?

$A$ small sphere of mass $m$ is suspended by a light and inextensible string of length $l$ from a point $O$ fixed on a smooth inclined plane of inclination $\theta$ with the horizontal. The sphere is moving in a circle on the incline as shown. If the sphere has a velocity $u$ at the top most position $A$, then:

$A$ 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 ......... $ms^{-1}$.

$A$ 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 $\sqrt{x(u^{2}-gL)}$. The value of $x$ is .............