A chain of mass M and length L is placed on a table, such that only a part of it is on the table and the remaining part hangs in air. If the coefficient of friction between the chain and table is `mu`, find the maximum length of the chain that can hang in air without the sliding of the part of the chain on the table.

The tensile strength of steel is 5 xx 10^7 N m^-2 . Find the maximum length of the wire that can hang vertically , without breking it. Densityof steel is 8 xx 10^3 kg m^-3.

A uniform disc of radius R, is resting on a table on its rim. The coefficent of friction between disc and table is mu (show in the figure). Now the disc is pulled with a force F . What is the maximum value of F for which the disc rolls without slipping?

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 piece of uniform string hangs vertically so that its free end just touches horizontal surface of a table. The upper end of the strig is now released. Show that at any instant during the falling of string, the total force on the surface is three times the weight of that part of string lying on the surface.

A pair of parallel horizontal conducting rails of negligible resistance shorted at one end is fixed on a table. The distance between the rails is L. A conducting massless rod of resistance R can slide on the rails frictionlessly. The rod is tied to a massless string which passes over a pulley fixed to the edge of the table, A mass m, tied to the other end of the string hanges vertically. A constant magnetic field B exists perpendicular to the table. If the system is released from rest, calculate. the acceleration of the mass at the instant when the velocity of the rod is half the terminal velocity.

A wire AB is carrying a steady current of 12A and is lying on the table. Another wire CD carrying 5A is held directly above AB at a height of 1mm. Find the mass per unit length of the wire CD so that it remains suspended at its position when left free. Give the direction of the current flowing in CD with respect to that in AB. [Take the value of g = 10ms^-2 ]

A pair of parallel horizontal conducting rails of negligible resistance shorted at one end is fixed on a table. The distance between the rails is L. A conducting massless rod of resistance R can slide on the rails frictionlessly. The rod is tied to a massless string which passes over a pulley fixed to the edge of the table, A mass m, tied to the other end of the string hanges vertically. A constant magnetic field B exists perpendicular to the table. If the system is released from rest, calculate. the terminal velocity achieved by the rod.

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 metal block of area 0.10 m^2 is connected to a 0.010 kg mass via a string that passes over an ideal pulley (considered massless and frictionless) as in fig.A liquid with a film thickness of 0.30 mm is placed between the block and the table.When released,the block moves ot the right with a constant speed of 00.085 m s^(-1) .Find the coefficient of viscosity of the liquid.

Two charged particles having charge 5 uC each are joined by an insulating string of length 1 m and the system is placed on a smooth horizontal table. Find the tension in the string.