Q23 of 29 Page 69

Two identical solid balls, one of ivory and the other of wet-clay, are dropped from the same height on the floor. Which one will rise to a greater height after striking the floor and why?

Ivory will rise to a greater height after striking the floor as ivory is more elastic in nature compared to wet clay ball.


When we drop the balls, they have equal potential energy stored it as they are at same height. Now once they are dropped, their potential energy starts getting converted into kinetic energy due to which they gain speed. Now after touching the floor, their kinetic energy makes them deformed and this energy is stored in elastic energy. Now as Ivory has high elasticity compared to wet-clay ball, therefore it is able to re-gain its same more easily and at a faster rate compared to wet clay ball. While re-gaining its shape, it pushes itself toward force and due to this ivory ball is able to reach higher compared to wet-clay ball.


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21

To what depth must a rubber ball be taken in deep sea so that its volume is decreased by 0.1%. (The bulk modulus of rubber is 9.8×108 N m-2; and the density of sea water is 103 kg m-3.)

Water density is 103 kg m-3.


 22

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 cable stretched? (Young’s modulus for steel is 2 × 1011 Nm-2.)

 24

Consider a long steel bar under a tensile stress due to force’s F acting at the edges along the length of the bar (Fig. 9.5). Consider a plane making an angle θ with the length. What are the tensile and shearing stresses on this plane?


(a) For what angle is the tensile stress a maximum?


(b) For what angle is the shearing stress a maximum?


 25

(a) A steel wire of mass μ per unit length with a circular cross section has a radius of 0.1 cm. The wire is of length 10 m when measured lying horizontal, and hangs from a hook on the wall. A mass of 25 kg is hung from the free end of the wire. Assuming the wire to be uniform and lateral strains << longitudinal strains, find the extension in the length of the wire. The density of steel is 7860 kg m-3(Young’s modules Y=2×1011 Nm-2).

(b) If the yield strength of steel is 2.5×108 Nm-2, what is the maximum weight that can be hung at the lower end of the wire?