$A$ particle of mass $M$ moves with constant speed along a circular path of radius $r$ under the action of a force $F$. Its speed is

$A$ 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

$A$ body of mass $m$ is moving with speed $V$ along a circular path of radius $r$. Now,the speed is reduced to $\frac{V}{2}$ and the radius is increased to $3r$. For this change,the initial centripetal force needs to be:

As shown in the figure, two equal masses hang on either side of a pulley at the same height from the ground. The mass on the right is given a horizontal speed $u$. After some time :-

With what frequency should a particle of mass $m$ be rotated so that a body of mass $M$ remains stationary?

$A$ particle starts from rest and performs circular motion of constant radius with speed given by $v = \alpha \sqrt{x}$,where $\alpha$ is a constant and $x$ is the distance covered. The correct graph of the magnitude of its tangential acceleration $(a_t)$ and centripetal acceleration $(a_c)$ versus $t$ will be: