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MECHANICAL PROPERTIES OF SOLIDS
Study Material
MECHANICAL PROPERTIES OF SOLIDS
Very Short Answer Questions
Q1. Define stress. Write its formula.
Q2. A copper wire of \(1\,\mathrm{mm}\) diameter is stretched by applying a force of \(10\,\mathrm{N}\). Find the stress in the wire.
Q3. Differentiate between tensile stress and compressive stress.
Q4. Define hydraulic stress.
Q5. Define strain. Write its formula.
Q6. A tungsten wire of length \(20\,\mathrm{cm}\) is stretched by \(0.1\,\mathrm{cm}\). Find the strain on the wire.
Q7. State Hooke's law of elasticity.
Q8. What are elastomers? Give examples.
Q9. What is the order of bulk modulus in the three states of matter?
Q10. Define compressibility? Mention its equation.
Q11. What is Poisson's ratio? State the Poisson ratio limits of steel.
Q12. Why steel is more elastic than rubber?
Q13. Why are sand heaps in pyramid-shape?
Q14. While constructing buildings and bridges, a pillar with distributed ends preferred to a pillar with rounded ends. Why?
Q15. Two identical solid balls, one of ivory and the other of wet clay, are dropped from the same height on to the floor. Which one will rise to a greater height after striking the floor? Why?
Q1. Define stress. Explain different types of stress with their dimensional formulas.
Q2. Define strain. Explain different types of strain.
Q3. What is elasticity? Explain different types of elastic moduli.
Q4. A brass wire of diameter \(1\,\mathrm{mm}\) and \(2\,\mathrm{m}\) is stretched by a force of \(20\,\mathrm{N}\). If the increase in length is \(0.51\,\mathrm{mm}\), find Young modulus of the wire.
Q5. A steel wire of length \(20\,\mathrm{cm}\) is stretched to increase its length by \(0.2\,\mathrm{cm}\). Find the lateral strain in the wire, if the Poisson's ratio for steel is \(0.19\).
Q6. Describe the behaviour of a wire under gradually increasing load.
Q7. Explain the concept of elastic potential energy in a stretched wire and hence obtain an expression for it.
Q8. Why is the maximum height of a mountain on Earth approximately \(10\,\mathrm{km}\)? Explain. \((\rho = 3 \times 10^3\,\mathrm{kg\,m^{-3}})\)
Q1. If an iron wire is stretched by \(1\%\), what is the strain on the wire?
Q2. A copper wire and an aluminium wire have lengths in the ratio \(3:2\), diameters in the ratio \(2:3\) and forces applied in the ratio \(4:5\). Find the ratio of increase in length of the two wires. \((Y_{\mathrm{Cu}}=1.1\times10^{11}\,\mathrm{N\,m^{-2}},\;Y_{\mathrm{Al}}=0.7\times10^{11}\,\mathrm{N\,m^{-2}})\)
Q3. A brass wire of cross-sectional area \(2\,\mathrm{mm^2}\) is suspended from a rigid support and a body of volume \(100\,\mathrm{cm^3}\) is attached to its other end. If the decrease in the length of the wire is \(0.11\,\mathrm{mm}\), when the body is completely immersed in water, find the natural length of the wire. \((Y_{\mathrm{brass}}=0.91\times10^{11}\,\mathrm{N\,m^{-2}},\;\rho_{\mathrm{water}}=10^3\,\mathrm{kg\,m^{-3}})\)
Q4. There are two wires of same material. Their radii and lengths are both in the ratio \(1:2\). If the extensions produced are equal, what is the ratio of loads?
Q5. Two wires of different material have same lengths and 'areas of cross-section. What is the ratio of their increase in length when forces applied are the same? \((Y_1=0.9\times10^{11}\,\mathrm{N\,m^{-2}},\;Y_2=3.6\times10^{11}\,\mathrm{N\,m^{-2}})\)
Q6. A metal wire of length \(2.5\,\mathrm{m}\) and area of cross section \(1.5\times10^{-6}\,\mathrm{m^2}\) is stretched through \(2\,\mathrm{mm}\). If its Young's modulus is \(1.25\times10^{11}\,\mathrm{N\,m^{-2}}\), find the tension in the wire.
Q7. An aluminium wire and a steel wire of the same length and cross-section are joined end-to-end. The composite wire is hung from a rigid support and a load is suspended from the free end. If the increase in length of the composite wire is \(1.35\,\mathrm{mm}\), find the ratio of the (i) stress in the two wires and (ii) strain in the two wires. \((Y_{\mathrm{Al}}=0.7\times10^{11}\,\mathrm{N\,m^{-2}},\;Y_{\mathrm{steel}}=2\times10^{11}\,\mathrm{N\,m^{-2}})\)
Q8. A \(2\,\mathrm{cm}\) cube of some substance has its upper face displaced by \(0.15\,\mathrm{cm}\) due to a tangential force of \(0.3\,\mathrm{N}\) while keeping the lower face fixed. Calculate the rigidity modulus of the substance.
Q9. A spherical ball of volume \(1000\,\mathrm{cm^3}\) is subjected to a pressure of \(10\) atmosphere. The change in volume is \(10^{-2}\,\mathrm{cm^3}\). If the ball is made of iron, find its bulk modulus. \((1\,\mathrm{atmosphere}=1\times10^5\,\mathrm{N\,m^{-2}})\)
Q10. A copper cube of side of length \(1\,\mathrm{cm}\) is subjected to a pressure of \(100\) atmosphere. Find the change in its volume if the bulk modulus of copper is \(1.4\times10^{11}\,\mathrm{N\,m^{-2}}\). \((1\,\mathrm{atm}=1\times10^5\,\mathrm{N\,m^{-2}})\)
Q11. Determine the pressure required to reduce the given volume of water by \(2\%\). Bulk modulus of water is \(2.2\times10^9\,\mathrm{N\,m^{-2}}\).
Q1. A structural steel rod has a radius of \(10\,\mathrm{mm}\) and a length of \(1.0\,\mathrm{m}\). A \(100\,\mathrm{kN}\) force stretches it along its length. Calculate (a) stress, (b) elongation, and (c) strain, given Young's modulus of structural steel is \(2.0\times10^{11}\,\mathrm{N\,m^{-2}}\).
Q2. A copper wire of length \(2.2\,\mathrm{m}\) and a steel wire of length \(1.6\,\mathrm{m}\), both of diameter \(0.5\,\mathrm{mm}\), are connected end to end. When stretched by a load, the net elongation is found to be \(0.70\,\mathrm{mm}\). Obtain the load applied.
Q3. In a human pyramid in a circus, the entire weight of the balanced group is supported by the legs of a performer who is lying on his back (as shown in Fig. 9.7). The combined mass of all the persons performing the act, and the tables, planks etc. involved is \(280\,\mathrm{kg}\). The mass of the performer lying on his back at the bottom of the pyramid is \(60\,\mathrm{kg}\). Each thigh bone (femur) of this performer has a length of \(50\,\mathrm{cm}\) and an effective radius of \(2.0\,\mathrm{cm}\). Determine the amount by which each thigh bone gets compressed under the load. The Young's modulus of bone is \(9.4\times10^9\,\mathrm{N\,m^{-2}}\).
Q4. A square lead slab of side \(50\,\mathrm{cm}\) and thickness \(10\,\mathrm{cm}\) is subject to a shearing force of \(9.0\times10^4\,\mathrm{N}\) as shown in Fig. 9.8. The lower edge is riveted to the floor. How much will the upper edge be displaced?
Q5. The average depth of Indian Ocean is about \(3000\,\mathrm{m}\). Calculate the fractional compression, \(\Delta V/V\), of water at the bottom of the ocean, given that the bulk modulus of water is \(2.2\times10^9\,\mathrm{N\,m^{-2}}\). (Take \(g=10\,\mathrm{m\,s^{-2}}\).)