A thin circular loop of radius R rotates about its vertical diameter with an angular frequency ` omega`. Show that a small bead on the wire loop rem ains at its lowermost point for `omega oversetlarrsqrt(g/R)` What is the angle made by the radius vector joining the centre to the bead with the vertical downward direction for `omega = sqrt (2g/R)`? neglect friction.

In a uniform magnetic field of induction B, a wire in the form of semicircle of radius r rotates about the diameter of the circle with angular frequency omega. If the total resistance of the circuit is R, the mean power generated per period of rotation is:

A disc of radius R is rotating with an angular speed omega_0 about a horizontal axis. it is placed on a horizontal table. The coefficient of kinetic friction is mu_k . What was the velocity of its centre of mass before being brought in contact with the table?

A circular coil of radius 8.0 cm and 20 turns is rotated about its vertical diameter with an angular speed of 50 rad s^-1 in a uniform horizontal magnetic field of magnitude 3.0xx10^-2 . Obtain themaximum and average emf induced in the coil. If the coil forms a closed loop of resistance 10 Omega , calculate the maximum value of current in the coil. Calculate the average power loss due to Joule heating. Where does this power come from?

A disc rotating about its axis with angular speed omega_0 is placed lightly (without any translational push) 011 a perfectly frictionless table. The radius of the disc is R. What are the linear velocities of the points A, B and C on the disc shown in Fig. 7.41? Will the disc roll in the direction indicated ?

A disc of radius R is rotating with an angular speed omega_0 about a horizontal axis. it is placed on a horizontal table. The coefficient of kinetic friction is mu_k . What condition should be satisfied for rolling to begin?

A disc of radius R is rotating with an angular speed omega_0 about a horizontal axis. it is placed on a horizontal table. The coefficient of kinetic friction is mu_k . Which force is responsible for the effects in what happens to the linear velocity of a point on its rim when placed in contact with the table? and What happens to the linear speed of the centre of mass when disc is placed in contact with the table?

A circular copper disc 10 cm in radius rotates at 20pi rad/s about an axis through its centre and perpendicular to the disc. A uniform magnetic field of 0.2 T acts perpendicular to the disc. What is the induced current if the resistance of the disc is 2Omega ?

A magnetic field in a certain region is given by bar B = B_0 cos omegathatk and a coil of radius a with resistanc R is placed i the XY-plane with its centre at the origin in the magnetic field as shown in the figure. Find the magnitude and direction of current at (a,0,0) at t = pi//2 omega

A magnet is suspended vertically from a fixed point by means of a spring, as shown in the figure. One end of the magnet hangs inside a coil of wire. The coil is connected in series with a resistance R. The magnet is displaced vertically a small distance D and the released. shown in the figure variation with time t of the vertical displacement d of the magnet from its equilibrium position. State and explain, by reference to electromagnetic induction, the nature of the oscillations of the magnet. Calculate the angular frequency omega_0 of the oscillations.

A compass needle free to turn in a horizontal plane is placed at the centre of circular coil of 30 turns and radius 12 cm. The coil is in a vertical plane making an angle of 45^@ with the magnetic meridian. When the current in the coil is 0.35 A, the needle points west to east. The current in the coil is reversed, and the coil is rotated about its vertical axis by an angle of 90^@ in the anticlockwise sense looking from above. Predict the direction of the needle. Take the magnetic declination at the places to be zero.