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 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 $$Y_{\text{Cu}} = 1.1 \times 10$$^{11}$$\ \mathrm{N\ m$$^{-2}$$}$$, $$Y_{\text{Steel}} = 2.0 \times 10$$^{11}$$\ \mathrm{N\ m$$^{-2}$$})$$

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

Q: A steel cable with a radius of $$1.5\ \mathrm{cm}$$ supports a chairlift. 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 tendency of a material to regain its original shape and size when the applied force is removed.

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 in the rod?

Accepted Answer

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

Question 3

Which equation correctly defines Young’s modulus ($$Y) $$for a material under tensile stress?

Accepted Answer

$$Y = \dfrac{F/A}{\Delta L/L}$$

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 $$Y_{	ext{Cu}} = 1.1 	imes 10$$^{11}$$\ \mathrm{N\ m$$^{-2}$$}$$, $$Y_{	ext{Steel}} = 2.0 	imes 10$$^{11}$$\ \mathrm{N\ m$$^{-2}$$})$$

Accepted Answer

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

Question 5

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

Accepted Answer

Hooke’s law is valid only in the linear region of the stress-strain curve.

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 lower edge is fixed, what is the displacement of the upper edge? (Shear modulus of lead $$G = 5.6 	imes 10^9$\ \mathrm{N\ m$$^{-2}$$})$$

Accepted Answer

$$0.16\ \mathrm{mm}$$

Question 7

Which modulus is relevant for describing the change in volume of a solid, liquid, or gas under uniform pressure?

Accepted Answer

Bulk modulus

Question 8

The ratio of lateral strain to longitudinal strain in a stretched wire is called:

Accepted Answer

Poisson’s ratio

Question 9

A steel cable with a radius of $$1.5\ \mathrm{cm}$$ supports a chairlift. 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 10

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

Accepted Answer

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

Question 11

A beam of length $$l$$, breadth $$b$$, and depth $$d is $$loaded at the center and supported at the ends. The sag at the center is given by:

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

Which of the following is NOT a correct statement about stress?

Accepted Answer

Stress is a vector quantity.

Question 14

A solid sphere is placed in a fluid under high pressure, causing a decrease in its volume but no change in shape. The strain produced is called:

Accepted Answer

Volume strain

Question 15

If the bulk modulus of water is $$2.2 	imes 10^9$\ \mathrm{N\ m$$^{-2}$$}$$ and the pressure at the bottom of the ocean is $$3 	imes 10^7$\ \mathrm{N\ m$$^{-2}$$}$$, what is the fractional compression $$\Delta V/V of $$water at that depth?

Accepted Answer

$$1.36 	imes 10$$^{-2}$$

Question 16

Which of the following materials is considered an elastomer?

Accepted Answer

Rubber

Question 17

The reciprocal of the bulk modulus is called:

Accepted Answer

Compressibility

Question 18

Which of the following best explains why beams in bridges often have an I-shaped cross-section?

Accepted Answer

To provide a large load-bearing surface and enough depth to prevent bending while reducing weight.

Mechanical Properties of Solids: Stress, Strain, and Elasticity

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