$A$ particle of mass '$m$' is rotating along a circular path of radius '$r$' having angular momentum '$L$'. The centripetal force acting on the particle is given by

In the figure,a body of mass $M$ rotates with an angular frequency of $2/\pi \text{ revolutions/sec}$. What is the tension produced in the string?

An object of mass $m$ moves with constant speed in a circular path of radius $R$ under the action of a force of constant magnitude $F$. The kinetic energy of the object is ............

Two particles of the same mass are moving in circular orbits because of a force given by $F(r) = -\frac{16}{r} - r^3$. The first particle is at a distance $r = 1$,and the second is at $r = 4$. The best estimate for the ratio of kinetic energies of the first and the second particle is closest to:

$A$ string of length $2 \ m$ can withstand a maximum tension of $16000 \ N$. $A$ particle of mass $2 \ kg$ is tied to one end of the string and rotated in a horizontal circle. What is the maximum number of rotations per second the particle can make so that the string does not break? (Take $\pi^2 = g = 10 \ m/s^2$)

$A$ ball of mass $0.25 \,kg$ attached to the end of a string of length $1.96 \,m$ is moving in a horizontal circle. The string will break if the tension is more than $25 \,N$. What is the maximum speed with which the ball can be moved (in $\,m/s$)?