A stone of mass m is tied to an elastic string of negligble mass andspring constant k. The unstretched length of the string is L andhas negligible mass. The other end of the string is fixed to a nail ata point P. Initially the stone is at the same level as the point P. Thestone is dropped vertically from point P.(a) Find the distance y from the top when the mass comes to restfor an instant, for the first time.(b) What is the maximum velocity attained by the stone in thisdrop?(c) What shall be the nature of the motion after the stone hasreached its lowest point?
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An equilateral triangle ABC is formed by two Cu rods AB and BCand one Al rod. It is heated in such a way that temperature ofeach rod increases by ΔT. Find change in the angle ABC.
A steel rod of length 2l, cross sectional area A and mass M is setrotating in a horizontal plane about an axis passing through thecentre. If Y is the Young’s modulus for steel, find the extension inthe length of the rod. (Assume the rod is uniform.)
A steel rod (Y = 2.0 × 1011 Nm–2; and α = 10–50 C–1) of length 1 mand area of cross-section 1 cm2 is heated from 0°C to 200°C, withoutbeing allowed to extend or bend. What is the tension produced inthe rod?
A wire of length L and radius r is clamped rigidly at one end. Whenthe other end of the wire is pulled by a force f, its length increasesby l. Another wire of the same material of length 2L and radius 2r,is pulled by a force 2f. Find the increase in length of this wire.
What is the Bulk modulus for a perfect rigid body?
What is the Young’s modulus for a perfect rigid body?
Identical springs of steel and copper are equally stretched. Onwhich, more work will have to be done?
Is stress a vector quantity?
The Young’s modulus for steel is much more than that for rubber.For the same longitudinal strain, which one will have greatertensile stress?
The Young’s modulus of steel is 2.0x10+11 w/m2. If the interatomic spacing for the
metal is 2.8x10-10m, find the increase in the interatomic spacing for a force of 109
N|m2 and the force constant?
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Which is more elastic rubber or steel? Explain.
Why is the force of repulsion responsible for the formation of a solid and not theforces of attraction?
Define modulus of elasticity and write its various types
An elastic wire is cut to half its original length. How would it affect the maximumload that the wire can support?
What are ductile and brittle materials?
State Hooke’s law?
The Marina trench is located in the Pacific Ocean, and at one place it is nearly eleven km beneath the surface of water. The water pressure at the bottom of the trench is about 1.1 × 108 Pa. A steel ball of initial volume 0.32 m3 is dropped into the ocean and falls to the bottom of the trench. What is the change in the volume of the ball when it reaches to the bottom?
Two strips of metal are riveted together at their ends by four rivets, each of diameter 6.0 mm. What is the maximum tension that can be exerted by the riveted strip if the shearing stress on the rivet is not to exceed 6.9 × 107 Pa? Assume that each rivet is to carry one quarter of the load.
A mild steel wire of length 1.0 m and cross-sectional area 0.50 × 10–2 cm2 is stretched, well within its elastic limit, horizontally between two pillars. A mass of 100 g is suspended from the mid-point of the wire. Calculate the depression at the midpoint.
A rod of length 1.05 m having negligible mass is supported at its ends by two wires of steel (wire A) and aluminium (wire B) of equal lengths as shown in Fig. 9.15. The cross-sectional areas of wires A and B are 1.0 mm2 and 2.0 mm2, respectively. At what point along the rod should a mass m be suspended in order to produce (a) equal stresses and (b) equal strains in both steel and aluminium wires.
How much should the pressure on a litre of water be changed to compress it by 0.10%?
Determine the volume contraction of a solid copper cube, 10 cm on an edge, when subjected to a hydraulic pressure of 7.0 ×106 Pa.
Compute the fractional change in volume of a glass slab, when subjected to a hydraulic pressure of 10 atm.
What is the density of water at a depth where pressure is 80.0 atm, given that its density at the surface is 1.03 × 103 kg m–3?
Compute the bulk modulus of water from the following data: Initial volume = 100.0 litre, Pressure increase = 100.0 atm (1 atm = 1.013 × 105 Pa), Final volume = 100.5 litre. Compare the bulk modulus of water with that of air (at constant temperature). Explain in simple terms why the ratio is so large.
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 cm2. Calculate the elongation of the wire when the mass is at the lowest point of its path.
. 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 steel cable with a radius of 1.5 cm supports a chairlift at a ski area. If the maximum stress is not to exceed 108 N m–2, what is the maximum load the cable can support?
A piece of copper having a rectangular cross-section of 15.2 mm × 19.1 mm is pulled in tension with 44,500 N force, producing only elastic deformation. Calculate the resulting strain?
Four identical hollow cylindrical columns of mild steel support a big structure of mass 50,000 kg. The inner and outer radii of each column are 30 cm and 60 cm respectively. Assuming the load distribution to be uniform, calculate the compressional strain of each column.
The edge of an aluminium cube is 10 cm long. One face of the cube is firmly fixed to a vertical wall. A mass of 100 kg is then attached to the opposite face of the cube. The shear modulus of aluminium is 25 GPa. What is the vertical deflection of this face?
Two wires of diameter 0.25 cm, one made of steel and the other made of brass are loaded as shown in Fig. 9.13. The unloaded length of steel wire is 1.5 m and that of brass wire is 1.0 m. Compute the elongations of the steel and the brass wires.
Read the following two statements below carefully and state, with reasons, if it is true or false.(a) The Young’s modulus of rubber is greater than that of steel;(b) The stretching of a coil is determined by its shear modulus.
The stress-strain graphs for materials A and B are shown in Fig. 9.12.
The graphs are drawn to the same scale. (a) Which of the materials has the greater Young’s modulus?(b) Which of the two is the stronger material?
Figure 9.11 shows the strain-stress curve for a given material. What are (a) Young’s modulus and (b) approximate yield strength for this material?
A steel wire of length 4.7 m and cross-sectional area 3.0 × 10–5 m2 stretches by the same amount as a copper wire of length 3.5 m and cross-sectional area of 4.0 × 10–5 m2 under a given load. What is the ratio of the Young’s modulus of steel to that of copper?