Elastic behaviour, stress-strain and Hooke's law — practice questions

Question 1 · difficulty L2 · understanding

The strain-stress plot for materials $A, B, C$ and $D$ is shown in the figure. Which material has the largest Young's modulus ?

• A. $B$
• B. $A$
• C. $D$
• D. $C$

Question 2 · difficulty L2 · understanding

An aluminium and steel rods having same lengths and cross-sections are joined to make total length of 120 cm at $30^{\circ} \mathrm{C}$. The coefficient of linear expansion of aluminium and steel are $24 \times 10^{-6} /{ }^{\circ} \mathrm{C}$ and $1.2 \times 10^{-5} /{ }^{\circ} \mathrm{C}$, respectively. The length of this composite rod when its temperature is raised to $100^{\circ} \mathrm{C}$, is $\_\_\_\_$ cm.

• A. 120.20
• B. 120.06
• C. 120.15
• D. 120.03

Question 3 · difficulty L2 · understanding

A copper wire of length 3 m is stretched by 3 mm by applying an external force. The volume of the wire is $600 \times 10^{-6} \mathrm{~m}^3$. The elastic potential energy stored in the wire in stretched condition would be $\_\_\_\_$ J. (Given Young modulus of copper $=1.1 \times 10^{11} \mathrm{~N} / \mathrm{m}^2$ )

Question 4 · difficulty L2 · understanding

A steel rod with y = 2.0 $$\times$$ 10 11 Nm $$-$$2 and $$\alpha$$ = 10 $$-$$5 $$^\circ$$C $$-$$1 of length 4 m and area of cross-section 10 cm 2 is heated from 0$$^\circ$$C to 400$$^\circ$$C without being allowed to extend. The tension produced in the rod is x $$\times$$ 10 5 N where the value of x is ____________.

Question 5 · difficulty L3 · understanding

A brass wire of length 2 m and radius 1 mm at $27^{\circ} \mathrm{C}$ is held taut between two rigid supports. Initially it was cooled to a temperature of $-43^{\circ} \mathrm{C}$ creating a tension $T$ in the wire. The temperature to which the wire has to be cooled in order to increase the tension in it to $1.4 T$, is $\_\_\_\_$ ${ }^{\circ} \mathrm{C}$.

• A. -71
• B. -80
• C. -65
• D. -86

Question 6 · difficulty L3 · understanding

A steel wire of length 2 m and Young's modulus $2.0 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$ is stretched by a force. If Poisson ratio and transverse strain for the wire are 0.2 and $10^{-3}$ respectively, then the elastic potential energy density of the wire is __________ $\times 10^5$ (in SI units).

Question 7 · difficulty L3 · understanding

The elastic potential energy stored in a steel wire of length $$20 \mathrm{~m}$$ stretched through $$2 \mathrm{~cm}$$ is $$80 \mathrm{~J}$$. The cross sectional area of the wire is __________ $$\mathrm{mm}^{2}$$. $$\left(\right.$$ Given, $$\left.y=2.0 \times 10^{11} \mathrm{Nm}^{-2}\right)$$

Question 8 · difficulty L3 · understanding

A thin rod having a length of $$1 \mathrm{~m}$$ and area of cross-section $$3 \times 10^{-6} \mathrm{~m}^{2}$$ is suspended vertically from one end. The rod is cooled from $$210^{\circ} \mathrm{C}$$ to $$160^{\circ} \mathrm{C}$$. After cooling, a mass $$\mathrm{M}$$ is attached at the lower end of the rod such that the length of rod again becomes $$1 \mathrm{~m}$$. Young's modulus and coefficient of linear expansion of the rod are $$2 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$$ and $$2 \times 10^{-5} \mathrm{~K}^{-1}$$, respectively. The value of $$\mathrm{M}$$ is __________ $$\mathrm{kg}$$. (Take $$\mathrm{g=10~m~s^{-2}}$$)

Question 9 · difficulty L3 · understanding

As shown in the figure, in an experiment to determine Young's modulus of a wire, the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of 45$$^\circ$$ with the load axis. The length of wire is 62.8 cm and its diameter is 4 mm. The Young's modulus is found to be $$x\times10^4$$ Nm$$^{-2}$$. The value of $$x$$ is ___________.

Question 10 · difficulty L3 · understanding

A square aluminum (shear modulus is $$25 \times 10^{9}\, \mathrm{Nm}^{-2}$$) slab of side $$60 \mathrm{~cm}$$ and thickness $$15 \mathrm{~cm}$$ is subjected to a shearing force (on its narrow face) of $$18.0 \times 10^{4}$$ $$\mathrm{N}$$. The lower edge is riveted to the floor. The displacement of the upper edge is ____________ $$\mu$$m.