Q: A steel rod of length $$1.0\ \mathrm{m}$$ and radius $$10\ \mathrm{mm} is $$stretched by a force of $$100\ \mathrm{kN}. $$What is the stress developed in the rod?

$$3.18 \times 10^8$\ \mathrm{N\ m$$^{-2}$$}$$

Q: A copper wire of length $$2.2\ \mathrm{m}$$ and a steel wire of length $$1.6\ \mathrm{m}$$, both of diameter $$3.0\ \mathrm{mm}$$, are connected end to end and stretched by a load. If the net elongation is $$0.70\ \mathrm{mm}$$, what is the load applied? (Given $$Y_{\mathrm{Cu}} = 1.1 \times 10$$^{11}$$\ \mathrm{N\ m$$^{-2}$$}$$, $$Y_{\mathrm{steel}} = 2.0 \times 10$$^{11}$$\ \mathrm{N\ m$$^{-2}$$})$$

$$1.8 \times 10^2$\ \mathrm{N}$$

Q: A lead slab of side $$50\ \mathrm{cm}$$ and thickness $$10\ \mathrm{cm} is $$subjected to a shearing force of $$9.0 \times 10^4$\ \mathrm{N}. If $$the shear modulus of lead is $$5.6 \times 10^9$\ \mathrm{N\ m$$^{-2}$$}$$, what is the displacement of the upper edge?

$$1.6 \times 10$$^{-4}$$\ \mathrm{m}$$

Q: A $$10\ \mathrm{cm}$$ edge copper cube is subjected to a hydraulic pressure of $$7.0 \times 10^6$\ \mathrm{Pa}. If $$the bulk modulus of copper is $$140 \times 10^9$\ \mathrm{N\ m$$^{-2}$$}$$, what is the volume contraction?

$$5.0 \times 10$$^{-8}$$\ \mathrm{m}^3$$

Q: A steel cable with a radius of $$1.5\ \mathrm{cm} is $$used in a ski lift. If the maximum allowable stress is $$1.0 \times 10^8$\ \mathrm{N\ m$$^{-2}$$}$$, what is the maximum load the cable can support?

$$7.1 \times 10^4$\ \mathrm{N}$$

Question 1

Which of the following best describes the property of elasticity in solids?

Accepted Answer

The ability of a material to regain its original shape and size after the removal of a deforming force.

Question 2

A steel rod of length $$1.0\ \mathrm{m}$$ and radius $$10\ \mathrm{mm} is $$stretched by a force of $$100\ \mathrm{kN}. $$What is the stress developed in the rod?

Accepted Answer

$$3.18 	imes 10^8$\ \mathrm{N\ m$$^{-2}$$}$$

Question 3

Which of the following statements about Hooke’s Law is correct?

Accepted Answer

It is valid only in the linear region of the stress-strain curve.

Question 4

A copper wire of length $$2.2\ \mathrm{m}$$ and a steel wire of length $$1.6\ \mathrm{m}$$, both of diameter $$3.0\ \mathrm{mm}$$, are connected end to end and stretched by a load. If the net elongation is $$0.70\ \mathrm{mm}$$, what is the load applied? (Given $$Y_{\mathrm{Cu}} = 1.1 	imes 10$$^{11}$$\ \mathrm{N\ m$$^{-2}$$}$$, $$Y_{\mathrm{steel}} = 2.0 	imes 10$$^{11}$$\ \mathrm{N\ m$$^{-2}$$})$$

Accepted Answer

$$1.8 	imes 10^2$\ \mathrm{N}$$

Question 5

Which modulus of elasticity is relevant for describing the response of a solid to a force applied parallel to its surface?

Accepted Answer

Shear modulus ($$G)$$

Question 6

A lead slab of side $$50\ \mathrm{cm}$$ and thickness $$10\ \mathrm{cm} is $$subjected to a shearing force of $$9.0 	imes 10^4$\ \mathrm{N}. If $$the shear modulus of lead is $$5.6 	imes 10^9$\ \mathrm{N\ m$$^{-2}$$}$$, what is the displacement of the upper edge?

Accepted Answer

$$1.6 	imes 10$$^{-4}$$\ \mathrm{m}$$

Question 7

The bulk modulus $$B of a $$material is defined as:

Accepted Answer

$$B = -\dfrac{p}{\Delta V/V}$$

Question 8

A $$10\ \mathrm{cm}$$ edge copper cube is subjected to a hydraulic pressure of $$7.0 	imes 10^6$\ \mathrm{Pa}. If $$the bulk modulus of copper is $$140 	imes 10^9$\ \mathrm{N\ m$$^{-2}$$}$$, what is the volume contraction?

Accepted Answer

$$5.0 	imes 10$$^{-8}$$\ \mathrm{m}^3$$

Question 9

Which of the following statements about Poisson’s ratio is correct?

Accepted Answer

It is the ratio of lateral strain to longitudinal strain and is dimensionless.

Question 10

A steel cable with a radius of $$1.5\ \mathrm{cm} is $$used in a ski lift. If the maximum allowable stress is $$1.0 	imes 10^8$\ \mathrm{N\ m$$^{-2}$$}$$, what is the maximum load the cable can support?

Accepted Answer

$$7.1 	imes 10^4$\ \mathrm{N}$$

Question 11

Which of the following best explains why steel is preferred over copper, brass, and aluminium in structural designs?

Accepted Answer

Steel has a higher Young’s modulus, requiring a larger force to produce the same strain.

Question 12

The elastic potential energy per unit volume stored in a stretched wire is given by:

Accepted Answer

$$u = \dfrac{1}{2} \sigma \epsilon$$

Question 13

A beam of length $$l$$, breadth $$b$$, and depth $$d is $$loaded at the centre. The sag $$\delta is $$given by:

Accepted Answer

$$\delta = \dfrac{W l^3$}{4 b d^3$ Y}$$

Question 14

Which of the following is NOT a correct statement about the mechanical properties of solids?

Accepted Answer

Bulk modulus is only relevant for solids.

Question 15

A mountain base is not under uniform compression but experiences shearing stress. If the elastic limit for a typical rock is $$30 	imes 10^7$\ \mathrm{N\ m$$^{-2}$$}$$, the density is $$3 	imes 10^3$\ \mathrm{kg\ m$$^{-3}$$}$$, and $$g = 10\ \mathrm{m\ s$$^{-2}$$}$$, what is the maximum height $$h of a $$mountain?

Accepted Answer

$$10\ \mathrm{km}$$

Question 16

Which of the following best describes the difference between elastic and plastic deformation?

Accepted Answer

Elastic deformation is reversible, while plastic deformation is permanent.

Mechanical Properties of Solids: Stress, Strain, and Elasticity

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