A simple pendulum of length I and mass m is suspended in a car that is travelling with a constant speed v around a circle of radius R. If the pendulum undergoes small oscillations about its equilibrium position, what will be its frequency•of oscillation ?

If a body is moving in a circle of radius r with a constant speed v m/s. Its angular velocity is

Obtain an expression for the centripetal force required to make a body of mass m moving with a constant speed v around a circular path of radius r.

The bob of a simple pendulum of length 1 m is' pulled aside from its equilibrium’ position through an angle 60^@ and released. Calculate the speed at which the bob passes the equilibrium position.

A body of radius R and mass m is rolling horizontally without slipping with a unifrom speed v. It then rolls up in an inclined plane to a maximum height of h. If h = (3v^2)/(4g) , determine the MI of the body about its axis of rotation.

A simple pendulum with a negatively charged bob is made to oscillate just above a positively charged plate. What happens to its time period?

A tuning fork oscillates 350 times in second. What is the distance travelled by the sound wave emitted by the tuning fork after its 5 oscillation. The speed of sound in air is 350 m/s

A bob of mass 0.1 kg hung from the ceiling of a room by a string 2 m long is set into oscillation. The speed of the bob at its mean position is 1 m s^1. What is the trajectory of the bob if the string is cut when the bob is (a) at one of its extreme positions, (b) at its mean position.

A solid cylinder of mass 20 kg rotates about its axis with angular speed 100 rad s-^1. The radius of the cylinder is 0.25 m. What is the kinetic energy associated with the rotation of the cylinder? What is the magnitude of angular momentum of the cylinder about its axis?

Given the M.I. of a dise of mass M and radius R about any of its diameter to be MR^2 /4. Find its M.I about an axis (i) passing through its centre and normal to it, and (ii) passing through a point at its edge and normal to it.

(a) Find the moment of inertia of a sphere about a tangent to the sphere, given the moment of inertia of the sphere about any of its diameters to be 2MR^2IS, where M is the mass of the sphere and R is the radius of the sphere(b) Given the moment of inertia of a disc of mass M and radius R about any of its diameters to be MR2I4, find its moment of inertia about an axis normal to the' disc and passing through a point on its edge.