$A$ particle of mass $m$ is rotating in a circular path of radius $r$. Its angular momentum is $L$. The centripetal force acting on it is $F$. The relation between $F$,$L$,$r$,and $m$ is

$A$ particle describes a horizontal circle of radius $r$ on the smooth surface of an inverted cone as shown. The height of the plane of the circle above the vertex is $h$. The speed of the particle should be

Two stones of masses $m$ and $3m$ are whirled in horizontal circles,the heavier one in a radius of $(r/3)$ and the lighter one in a radius of $r$. The tangential speed of the lighter stone is $n$ times that of the heavier stone when they experience the same centripetal force. The value of $n$ is:

$A$ particle of mass $m$ is rotating in a plane in a circular path of radius $r$. Its angular momentum is $L$. The centripetal force acting on the particle is:

$A$ particle rotates in a horizontal circle of radius $R$ in a conical funnel with constant speed $V$. The inner surface of the funnel is smooth. The height of the plane of the circle from the vertex of the funnel is (where $g$ is the acceleration due to gravity):

$A$ mass of $100\, g$ is tied to one end of a string $2\, m$ long. The body is revolving in a horizontal circle making a maximum of $200$ revolutions per minute. The other end of the string is fixed at the center of the circle of revolution. The maximum tension that the string can bear is .......... $N$ (approximately).