$A$ conical pendulum is moving in a circle with angular velocity $\omega$ as shown. If the tension in the string is $T$, which of the following equations is correct?

$A$ body of mass $M = 100 \; g$ is rotating in a horizontal circle with an angular frequency of $n = 2/\pi \; \text{rev/sec}$ as shown in the figure. If the radius of the circular path is $R = 1 \; m$, what is the angle $\theta$ made by the string with the vertical? $(g = 10 \; m/s^2)$

Two particles of mass $2m$ and $m$ are attached to a light string as shown. The complete system is rotated in a horizontal circle with a constant angular velocity $2\omega$ about an axis passing through point $O$ and perpendicular to the plane of the circle. Find the ratio $T_{OA} / T_{AB}$,where $T_{OA}$ and $T_{AB}$ are the tensions in strings $OA$ and $AB$ respectively.

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

$A$ dumbbell is placed on a frictionless horizontal table. Sphere $A$ is attached to a frictionless pivot so that $B$ can be made to rotate about $A$ with constant angular velocity. If $B$ (mass $2M$) makes one revolution in period $P$,the tension in the rod (length $d$) is

Assume a proton is rotating along a circular path of radius $1 \,m$ under a centrifugal force of $4 \times 10^{-12} \,N$. If the mass of the proton is $1.6 \times 10^{-27} \,kg$, then its angular velocity of rotation is