Three particles of equal mass are tied to a string and rotated in a horizontal plane as shown. What is the ratio of tensions in the three parts of the string?

$A$ particle of mass $m$ is suspended from a ceiling through a string of length $L$. If the particle moves in a horizontal circle of radius $r$ as shown in the figure,then the speed of the particle is

$A$ proton of mass $1.6 \times 10^{-27} \, kg$ moves in a circular orbit of radius $0.10 \, m$ under a centripetal force of $4 \times 10^{-13} \, N$. The frequency of revolution of the proton is about:

Two particles of mass $m$ are constrained to move along two horizontal frictionless rails that make an angle $2\theta$ with respect to each other. They are connected by a spring with spring constant $k$. The angular frequency of small oscillations for the motion where the two masses always stay at the same distance from the meeting point of the rails 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

$A$ bob of mass $m$ is whirled in a horizontal plane by means of a string of length $\ell$ with an initial angular speed of $\omega$. The tension in the string is $T$. If the angular speed becomes $2\omega$ while keeping the same radius $\ell$,the tension in the string becomes: