A ductile metal wire has resistance R. What will be the resistance of this wire in terms of R is it is stretched to three times its original length, assuming the density and resistivity of the material do not change when the wire is stretched?

The space between two 15-in.-long concentric cylinders is filled with glycerin (viscosity = 8.5 × 10-3 lb·s/ft2). the inner cylinder has a radius of 1 in. and the gap width between cylinders is 0.1 in. determine (a) the torque and (b) the power required to rotate the inner cylinder at 180 rev/min. the outer cylinder is fixed. assume the velocity distribution in the gap to be linear.