A cone-shaped funnel is being rotated with constant angular velocity `omega` An object is placed on the inner wall of the funnel. The object can freely move along the generatrlx of the cone, but during the motion of the funnel the body is in a state of equilibrium. Is this equilibrium stable or unstable?

A horizontally oriented uniform disc of mass M and radius R rotates freely about a stationary vertical axis passing through its centre. The disc has a radial guide along which can slide without friction a small body of mass m . A light thread running down through the hollow axle of the disc is tied to the body initially the body was located at the edge of the disc and the whole system rotated with ann angular velocity omega_(0) . Then by means of a force F applied to the lower and of the thread the body was slowly pulled to the rotation axis. find: (a). The angular velocity of the system in its final state. (b). The work performed by the force F.

A particle is at rest with respect to the wall of an inverted cone rotating with uniform angular velocity omwega about its central axis. The displacement of particle along the surface up or down, the equilibrium of particle is

A very small cube of mass m is placed on the inside of a conial funnelof semivertical angle (pi//2-theta) . The funnel is then set in rotation. If the coefficient of static friction between the cube and the funnel is mu and the centre of the cube is at a distance r from the axis of rotation, what are the largest and smallest angular velocities with which the funnel can be rotated so that the block will not move with respect to the funnel ?

A wheel is revolving at an angular speed of omega . A pin welded at the circumference of the wheel forces a T shaped body to move up and down. The pin slides freely inside the slot of the yoke as the wheel rotates. The T shaped body is constrained to move vertically by a set of walls (a) Find the time period of oscillatory motion of point A at the base of the T shaped body (b) Is the motion of A simple harmonic?

A weightless horizontal rigid rod along which two balls of the same mass m can move without friction rotates at a constant angular velocity omega about a vertical axle. The balls are connected by a weightless spring of rigidity k, whose length in the undeformed state is l_(0) . The ball which is closer to the vertical axle is connected to it by he same spring. Determine the lengths of the springs. Under what conditions will be balls move in circles ?

A light rod AB is fitted with a small sleeve of mass m which can slide smoothly over it. The sleeve is connected to the two ends of the rod using two springs of force constant 2k and k (see fig). The ends of the springs at A and B are fixed and the other ends (connected to sleeve) can move along with the sleeve. The natural length of spring connected to A is l_(0) . Now the rod is rotated with angular velocity w about an axis passing through end A that is perpendicular to the rod. Take (k)/(momega^(2)) = eta and express the change in length of each spring (in equilibrium position of the sleeve relative to the rod) in terms of l_(0) and eta .

A very small cube of mass 2kg is placed on the surface of a funnel as shown in figure. The funnel is rotating about its vertical axis of symmetry with angular velocity omega . The wall of funnel makes an angle 37^(@) with horizontal. The distance of cube from the axis of rotation is 20 cm and friction coefficient is mu (Take g = 10 m//s^(2) ) The mimimum value of angular velocity for which relative slipping occurs and also the direction of frictional force acting mu = 2//3 :

A very small cube of mass 2kg is placed on the surface of a funnel as shown in figure. The funnel is rotating about its vertical axis of symmetry with angular velocity omega . The wall of funnel makes an angle 37^(@) with horizontal. The distance of cube from the axis of rotation is 20 cm and friction coefficient is mu (Take g = 10 m//s^(2) ) The maximum value of angular velocity for which no relative slipping occur and also direction of frictional force is : (take mu = 2//3 )