As per the given figure,to complete the circular loop,what should be the radius if the initial height is $5 \, m$ (in $, m$)?

$A$ small body slides down a smooth uneven surface from a height $H$,which eventually emerges into a circular loop of radius $R (< H)$. What should be the value of $H$,so that the force on the body at $A$ is $\sqrt{2}$ times its weight?

An object is at the top of a smooth sphere which is kept fixed. As the object slides down after being given a negligible side push,what is the behavior of the magnitude of the acceleration of the object during its motion until it reaches the ground?

$A$ particle originally at rest at the highest point of a smooth vertical circle is slightly displaced. It will leave the circle at a vertical distance $h$ below the highest point,such that

$A$ 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 $\,m/s^2$)

$A$ stone of mass $m$,tied to a string,is being whirled in a vertical circle with a uniform speed. The tension in the string is