Introductory Exercise 12.1
Ques 1: Two wires A and B of same dimensions are stretched by same amount of force. Young's modulus of A is twice that of B. Which wire will get more elongation?
Sol:
as Young's modulus of A is twice of B, so elongation of A will be half of B.
Ques 2: A rod 100 cm long and of 2 cm × 2 cm crosssect ion is subjected to a pull of 1000 kg force. If the modulus of elasticity of the material is 2.0 × 10^{6} kg/cm^{2}, determine the elongation of the rod.
Sol:
Ques 3: A cast iron column has internal diameter of 200 mm. What should be the minimum external diameter so that it may carry a load of 1.6 MN without the stress exceeding 90 N/mm^{2}?
Sol:
= 0250 = 250 mm
EXERCISES
For JEE Main
Subjective Questions
Ques 1: A cylindrical steel wire of 3 m length is to stretch no more than 0.2 cm when a tensile force of 400 N is applied to each end of the wire. What minimum diameter is required for the wire?
Y_{steel} =2.1 × 10^{11} N/m^{2}
Sol:
= 1.9 × 10^{3} m = 1.9 mm
Ques 2: The elastic limit of a steel cable is 3.0 × 10^{8} N/m^{2} and the crosssection area is 4cm^{2}. Find the maximum upward acceleration that can be given to a 900 kg elevator supported by the cable if the stress is not to exceed onethird of the elastic limit.
Sol:
Ques 3: If the elastic limit of copper is 1.5 x 10^{8}N/m^{2}, determine the minimum diameter a copper wire can have under a load of 10.0 kg, if its elastic limit is not to be exceeded.
Sol:
Ques 4: Find the increment in the length of a steel wire of length 5 m and radius 6 mm under its own weight. Density of steel = 8000 kg/m^{3} and Young's modulus of steel = 2 x 10^{11} N/m^{2}. What is the energy stored in the wire? (Take g = 9.8m/s^{2})
Sol:
= 49 × 10^{6} m
Ques 5: Two wires shown in figure are made of the same material which has a breaking stress of 8 × 10^{8} N/m^{2}. The area of crosssection of the upper wire is 0.006 cm^{2} and that of the lower wire is 0.003 cm . The mass m_{1} = 10 kg, m_{2} = 20 kg and the hanger is light. Find the maximum load that can be put on the hanger without breaking a wire. Which wire will break first if the load is increased? (Take g = 10 m/s^{2})
Sol:
= 48  30 = 18 kg
So, lower wire will break if m > 14 kg. i.e., maximum load which can be put on hanger without breaking wire is 14 kg.
Ques 6: A steel wire and a copper wire of equal length and equal crosssectional area are joined end to end and the combination is subjected to a tension. Find the ratio of:
(a) the stresses developed in the two wires,
(b) the strains developed. (Y of steel =2 × 10^{11} N/m^{2} and T of copper = 1.3 × 10^{11} N/m^{2})
Sol: F/A is same as both have same crosssection area and subjected under same tension.
Ques 7: Calculate the approximate change in density of water in a lake at a depth of 400 m below the surface. The density of water at the surface is 1030 kg/m^{3} and bulk modulus of water is 2 × 10^{9}N/m^{2}.
Sol:
Ques 8: A wire of length 3 m, diameter 0.4 mm and Young's modulus 8 × 10^{10} N/m^{2} is suspended from a point and supports a heavy cylinder of volume 10^{3} m^{3} at its lower end. Find the decrease in length when the metal cylinder is immersed in a liquid of density 800 kg/m^{3}.
Sol:
= 2.39 × 10^{3} m
Ques 9: In taking a solid ball of rubber from the surface to the bottom of a lake of 180 m depth, reduction in the volume of the ball is 0.1%. The density of water of the lake is 1 × 10^{3} kg/m . Determine the value of the bulk modulus of elasticity of rubber. (g = 9.8m/s^{2})
Sol:
= 1.76 × 10^{9} N/m^{2}
Ques 10: A sphere of radius 10 cm and mass 25 kg is attached to the lower end of a steel wire of length 5 m and diameter 4 mm which is suspended from the ceiling of a room. The point of support is 521 cm above the floor. When the sphere is set swinging as a simple pendulum, its lowest point just grazes the floor. Calculate the velocity of the ball at its lowest position. (Y_{steel} =2 × 10^{11} N/m^{2})
Sol:
118 videos470 docs189 tests

1. What is elasticity and why is it important in physics? 
2. How is elasticity measured and what are its units? 
3. What are some reallife applications of elasticity? 
4. How does temperature affect the elasticity of materials? 
5. Can elasticity be permanent? 
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