A 0.5 kg mass is suspended vertically from a point fixed on the Earth by a spring having a stiffness of 5 N/mm. What is its static displacement in (mm and m)? Solve by changing the unit into 'm' as well as 'mm'.

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 body of mass m is attached to one end of a massless spring which is suspended vertically from a fixed point. The mass is held in hand so that the spring is neither stretched nor compressed. Suddenly the support of the hand is removed. The lowest position attained by the mass during oscillation is 4 cm below the point, where it held in hand. What is the amplitude of oscillation?

A body of mass m is attached to one end of a massless spring which is suspended vertically from a fixed point. The mass is held in hand so that the spring is neither stretched nor compressed. Suddenly the support of the hand is removed. The lowest position attained by the mass during oscillation is 4 cm below the point, where it held in hand. Find the frequency of oscillation?

A straight horizontal conducting rod of length 0.45 m and mass 60 g is suspended by two vertical wires at its ends. A current of 5.0 A is set up in the rod through the wires. What will be the total tension in the wires if the direction of current is reversed keeping the magnetic field same as before? (Ignore the mass of the wires.) g = 9.8 m s^-2 .

A straight horizontal conducting rod of length 0.45 m and mass 60 g is suspended by two vertical wires at its ends. A current of 5.0 A is set up in the rod through the wires. What magnetic field should be set up normal to the conductor in order that the tension in the wires is zero?

A body of mass 6 kg is kept at a height of 5 m from the surface of earth. Find the potential energy of the body.

Two bodies of masses 1 kg and 3 kg respectively are connected rigidly by a vertical spring. The body of mass 3 kg rests on a smooth horizontal surface. The force constant of the spring is 484Nm^(-1) . From the equilibrium position, the mass of 1 kg is displaced vertically through a distance of 0.02 m and then released. calculate (i) and frequency of oscillation of the mass of 1 kg (ii) the maximum velocity of this mass (iii) its oscillation energy and (iv) the reaction of the table on the mass of 3 kg, when mass 1 kg is having harmonic oscillations.

A truck is pulling a car out of a ditch by means of a steel cable that is 9.1 m long and has a radius of 5 mm. When the car just begins to move, the tension in the cable is 800 N. How much has the cble streched ? (Young's modulus for steel is 2xx 10^11 N m^-2) .

Two pith-balls each of mass 5xx10^-4 kg are suspended from the same point by silk threads 0.2 m long equal charges are given to the balls, which separate, until the threads enclose an angle of 30^@ , Calculate the charge on each pith-ball.