A uniform rope of length 12 m amd mass 6 kg hangs vertically from a rigid support.A block of mass 2 kg is attached to the free end of the rope.A transverse pulse of wave length 0.06m is produced at the lower end of the rope.What is the wavelength of the pulse when it reaches the top of the rope?

A rigid bar of mass 15 kg is supported symmetrically by three wires each 2.0 m long. Those at each end are of copper and the middle one is of iron. Determine the ratio of their diameters if each is to have the same tension.

A 14.5 kg mass, fastened to the end of a steel wire of unstretched length 1.0 m, is whirled in a vertical circle with an angular velocity of 2 rev/s at the bottom of the circle. The cross-sectional area of the wire is 0.065 cm^2 . Calculate the elongation of the wire when the mass is at the lowest point of its path.

A bolt of mass 0.3 kg falls from the ceiling of an elevator moving down with an uniform speed of 7 m s^-1 . It hits the floor of the elevator (length of the elevator = 3 m) and does not- rebound. What is the heat produced by the impact? Would your answer be different if the elevator were stationary?

The velocity of transverse wave passing through a string of length 3m is 16 m/sec.If the mass of the string is 0.15 kg,find (i)the tension of the string,(ii)the frequency of its fundamental and (iii)the wavelength.

A monkey of mass 40 kg climbs on a rope (Fig. 5.20) which can stand a maximum tension of 600 N. In which of the following cases will the rope break: the monkey (a) climbs up with an acceleration of 6 m s^2 (b) climbs down with an acceleration of 4 m s^2 (c) climbs up with a uniform speed of 5 m s^1 (d) falls down the rope nearly freely under gravity? (Ignore the mass of the rope).

A copper wire is held at two ends by rigid supports.At 30^0 C the wire is just taut,with negligble tension.Find the speed of transverse wave in the wire at 10^0 C[ alpha =1.7xx(10)^-5/^0C , gamma=1.3xx(10)^11N/(m)^2 , rho=9xx(10)^3kg/(m)^3 ]