What space must be left between two rails 60 m long so as to allow for an expansion upto `40^@C` assuming that the rails are laid down at `15^@C, alpha = 0.000012`?

The radius of curvature of a railway line at a place is 40000m.the train is running at 20 m s^-1 .the distance between the two rails is 1.5 m.Find the elevation of the outer rail over the inner one so that the train may be able to run safely.

What mass of NaCl must be dissolved in 65.0 g of water to lower the freezing point of water by 7.50^@C ? The freezing point depression constant (k_f) for water is 1.86^@C/m . Assume that Van't Hoff factor for NaCl is 1.87. (Molar mass of NaCl =58.5g).

A railway track running North South has two parallel rails 1.0m apart. Calculate the value of induced e.m.f. between the rails when a train passes at a speed of 90 kmh(-1) . Horizontal component of earth’s field at that place is 0.3xx1O(-4) Wbm(-2) and angle of dip is 60^@ .

A brass wire 1.8 m long at 27^@C is held when taut with little tension between two rigid supports. If the wire is cooled to a temperature - 39^@C , what is the tension developed in the wire, if tis diameter is 2.0 mm? Coefficient of linar expansion of brass = 2.0 xx 10^5 ^@C^-1 , Young's modulus of brass = 0.91 xx 10^11 Pa .

Figure shows a metal rod PQ resting on the smooth rails AB and positioned between the poles of a permanent magnet. The rails, the rod, and the magnetic field are in three mutual perpendicular directions. A galvanometer G connects the rails through a switch K. Length of the rod =15 cm, B = 0.50 T, resistance of the closed loop containing the rod = 9.0 mOmega Assume the field to be uniform. What is the induced emf in the moving rod if the magnetic field is parallel to the rails instead of being perpendicular? :

Figure shows a metal rod PQ resting on the smooth rails AB and positioned between the poles of a permanent magnet. The rails, the rod, and the magnetic field are in three mutual perpendicular directions. A galvanometer G connects the rails through a switch K. Length of the rod =15 cm, B = 0.50 T, resistance of the closed loop containing the rod = 9.0 mOmega . Assume the field to be uniform and the rod is moved with a speed of 12 cm/s. How much power is dissipated as heat in the closed circuit? What is the source of this power? :

Figure shows a metal rod PQ resting on the smooth rails AB and positioned between the poles of a permanent magnet. The rails, the rod, and the magnetic field are in three mutual perpendicular directions. A galvanometer G connects the rails through a switch K. Length of the rod =15 cm, B = 0.50 T, resistance of the closed loop containing the rod = 9.0 mOmega Assume the field to be uniform. What is the retarding force on the rod when K is closed? :

Figure shows a metal rod PQ resting on the smooth rails AB and positioned between the poles of a permanent magnet. The rails, the rod, and the magnetic field are in three mutual perpendicular directions. A galvanometer G connects the rails through a switch K. Length of the rod =15 cm, B = 0.50 T, resistance of the closed loop containing the rod = 9.0 mOmega Assume the field to be uniform. Is there an excess charge built up at the ends of the rods when K is open? What if K is closed? :

An ironring which is 1 m in diameter is to be shrunk on a pulley which is 1.005 m in diameter. If the temprature of the ring is 10^@C , find the temperature to which it must be raised so as that it will just slip on the circumferences on the pulley, alpha for iron = 0.00012 .