MECHANICAL PROPERTIES OF SOLIDS

Very Short Question Answers

Q1. State Hooke's law of elasticity.

Ans.

Hooke’s law of elasticity: With in elastic limit, the stress is directly proportional to strain.

$Stress \propto strain$

$stress\, =\, K\, (strain)$


Q2. State the units and dimensions of stress.

Ans.

S.I Unit- $Pascal$ ,(or) $N/\,m^{2}$ Dimensional Formula :$\,\,[M^{1}\,L^{-1}\,T^{-2}\,]$


Q3. State the units and dimensions of modulus of elasticity.

Ans.

S.I Unit- $Pascal$ ,(or) $N/\,m^{2}$ Dimensional Formula :$\,\,[M^{1}\,L^{-1}\,T^{-2}\,]$


Q4. State the units and dimensions of Young's modulus.

Ans.

S.I Unit- $Pascal$ ,(or) $N/\,m^{2}$ Dimensional Formula :$\,\,[M^{1}\,L^{-1}\,T^{-2}\,]$


Q5. State the units and dimensions of modulus of rigidity.

Ans.

S.I Unit- $Pascal$ ,(or) $N/\,m^{2}$ Dimensional Formula :$\,\,[M^{1}\,L^{-1}\,T^{-2}\,]$


Q6. State the units and dimensions of Bulk modulus.

Ans.

S.I Unit- $Pascal$ ,(or) $N/\,m^{2}$ Dimensional Formula :$\,\,[M^{1}\,L^{-1}\,T^{-2}\,]$


Q7. State the examples of nearly perfect elastic and plastic bodies.

Ans.

Nearly perfect elastic bodies: quartz, phosphor – bronze,
Nearly perfect plastic bodies: clay, putty, dough, butter. 


Short Question Answers

Q1. Define Hooke's Law of elasticity, proportionality limit, permanent set and breaking stress.

Ans. MECHANICAL PROPERTIES OF SOLIDS


Q2. Define modulus of elasticity, stress, strain and Poisson's ratio.

Ans. MECHANICAL PROPERTIES OF SOLIDS


Q3. Define Young's modulus, Bulk modulus and Shear modulus.

Ans. MECHANICAL PROPERTIES OF SOLIDS


Q4. Define stress and explain the types of stress.

Ans. MECHANICAL PROPERTIES OF SOLIDS


Q5. Define strain and explain the types of strain.

Ans. MECHANICAL PROPERTIES OF SOLIDS


Q6. Define strain energy and derive the equation for the same.

Ans. MECHANICAL PROPERTIES OF SOLIDS


Q7. Explain why steel is preferred to copper. brass, aluminium in heavy-duty machines and in structural designs.

Ans. MECHANICAL PROPERTIES OF SOLIDS


Q8. Describe the behaviour of a wire under gradually increasing load.

Ans. MECHANICAL PROPERTIES OF SOLIDS


Q9. Two identical solid balls, one of Ivory and the other of wet-clay are dropped from the same height onto the floor. Which one will rise to a greater height after striking the floor and why?

Ans. MECHANICAL PROPERTIES OF SOLIDS


Q10. While constructing buildings and bridges a pillar with distributed ends is preferred to a pillar with rounded ends. Why?

Ans. MECHANICAL PROPERTIES OF SOLIDS


Q11. Explain why the maximum height of a mountain on earth is approximately 10 km?

Ans. MECHANICAL PROPERTIES OF SOLIDS


Q12. Explain the concept of Elastic Potential Energy in a stretched wire and hence obtain the expression for it.

Ans. MECHANICAL PROPERTIES OF SOLIDS


Essay Question Answers

Q1. Define Hooke's law of elasticity and describe an experiment to determine the Young's modulus of the material of a wire.

Ans. MECHANICAL PROPERTIES OF SOLIDS


Problems Question Answers

Q1. A copper wire of 1mm diameter is stretched by applying a force of 10N. Find the stress in the wire.

Ans. MECHANICAL PROPERTIES OF SOLIDS


Q2. A tungsten wire of length 20 cm is stretched by 0.1 em. Find the strain on the wire

Ans. MECHANICAL PROPERTIES OF SOLIDS


Q3. If an iron wire is stretched by 19%, what is the strain on the wire?

Ans. MECHANICAL PROPERTIES OF SOLIDS


Q4. A brass wire of diameter 1mm and length 2 m is streched by applying a force of 20N. If the increase in length is 0.51 mm. find (i) the stress, (i) the strain and (ii) the Young's modulus of the wire.

Ans. MECHANICAL PROPERTIES OF SOLIDS


Q5. 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.

Ans. MECHANICAL PROPERTIES OF SOLIDS


Q6. A brass wire of cross-sectional area 2 mm² is suspended from a rigid support and a body of volume 100 cm' is attached to its other end. If the decrease in the length of the wire is 0.11 mm, when the body is completely immersed in water, find the natural length of the wire.

Ans. MECHANICAL PROPERTIES OF SOLIDS


Q7. 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?

Ans. MECHANICAL PROPERTIES OF SOLIDS


Q8. 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?

Ans. MECHANICAL PROPERTIES OF SOLIDS


Q9. A metal wire of length 2.5 m and area of cross section 1.5 x 10 m² is stretched through 2 mm. If its Young's modulus is 1.25 x 10 N.m. find the tension in the wire.

Ans. MECHANICAL PROPERTIES OF SOLIDS


Q10. 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 1.35mm, find the ratio of the (1) stress in the two wires and (ii) strain in the two wires. (Y=0.7 x 10 Nm. Y = 2x 10 Nm³)

Ans. MECHANICAL PROPERTIES OF SOLIDS


Q11. A 2 cm cube of some substance has its upper face displaced by 0.15 cm due to a tangential force of 0.3 N while keeping the lower face fixed. Calculate the rigidity modulus of the substance.

Ans. MECHANICAL PROPERTIES OF SOLIDS


Q12. A spherical ball of volume 1000 cm³ is subjected to a pressure of 10 Atmosphere. The change in volume is 10 cm³. If the ball is made of iron. find its bulk modulus.

Ans. MECHANICAL PROPERTIES OF SOLIDS


Q13. A copper cube of side of length 1 cm is subjected to a pressure of 100 atmosphere. Find the change in its volume if the bulk modulus of copper is 1.4 x 10 Nm (1 atm = 1 x 10 Nm)

Ans. MECHANICAL PROPERTIES OF SOLIDS


Q14. Determine the pressure required to reduce the given volume of water by 2%. Bulk modulus of water is 2.2 x 10 Nm

Ans. MECHANICAL PROPERTIES OF SOLIDS


Q15. A steel wire of length 20 cm is stretched to increase its length by 0.2 cm. Find the lateral strain in the wire if the Poisson's ratio for steel is 0.19.

Ans. MECHANICAL PROPERTIES OF SOLIDS