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Two similar wires under the same load yield elongation of 0.1 mm and 0.05 mm respectively. If the area of cross-section of the wire is $4 {\mathrm{mm}}^2$, then the area of cross-section of the second wire is
1. $6 {\mathrm{mm}}^2$
2. $8 {\mathrm{mm}}^2$
3. $10 {\mathrm{mm}}^2$
4. $12 {\mathrm{mm}}^2$

If the ratio of diameters, length and Young's modulus of steel and copper wire shown in the figure are p, q and s respectively, then the corresponding ratio of increase in their lengths would be

1. $\frac{5q}{(7 s{p}^2)}$
2. $\frac{7q}{\left(5s{p}^2\right)}$
3. $\frac{2q}{(5 sp)}$
4. $\frac{7q}{(5 sp)}$

A steel ring of radius \(\mathrm{r}\) and cross-section area \(\mathrm{A}\) is fitted onto a wooden disc of radius \(\mathrm{R}(\mathrm{R}>\mathrm{r}).\) If Young's modulus is \(\mathrm{E},\) then the force with which the steel ring is expanded is:

A wire of length L is hanging from a fixed support. The length changes to ${\mathrm{L}}_1 \mathrm{and} {\mathrm{L}}_2$ when masses ${\mathrm{M}}_1 \mathrm{and} {\mathrm{M}}_2$ are suspended respectively from its free end. Then L is equal to
1. $\frac{{\mathrm{L}}_1+{\mathrm{L}}_2}{2}$
2. $\sqrt{{\mathrm{L}}_1{\mathrm{L}}_2}$
3. $\frac{{\mathrm{L}}_1{\mathrm{M}}_2+{\mathrm{L}}_2{\mathrm{M}}_1}{{\mathrm{M}}_1+{\mathrm{M}}_2}$
4. $\frac{{\mathrm{L}}_1{\mathrm{M}}_2-{\mathrm{L}}_2{\mathrm{M}}_1}{{\mathrm{M}}_2-{\mathrm{M}}_1}$

A uniform plank of Young's modulus Y is moved over a smooth horizontal surface by a constant horizontal force F. The area of cross-section of the plank is A. The compressive strain on the plank in the direction of the force is :
1. (F/AY)
2. 2(F/AY)
3. $\frac{1}{2}$(F/AY)
4. 3(F/AY)

Young's modulus of rubber is ${10}^{4}N/m^2$ and area of cross-section is $2 {\mathrm{cm}}^2$. If the force of $2\times {10}^5$ dynes is applied along its length, then its initial length L becomes :
1. 3L
2. 4L
3. 2L
4. None of the above

If the Young's modulus of the material is 3 times its modulus of rigidity, then its volume elasticity will be :
1. Zero
2. Infinity
3. $2\times {10}^{10}N/m^2$
4. $3\times {10}^{10}N/m^2$

A light rod of length 2m is suspended from the ceiling horizontally by means of two vertical wires of equal length. A weight W is hung from the light rod as shown in the figure. The rod is hung by means of a steel wire of cross-sectional area $A_1=0.1$ $c{m}^2$ and brass wire of cross-sectional area $A_2=0.2$ $c{m}^2$. To have equal stress in both wires, ${\mathrm{T}}_1/{\mathrm{T}}_2$=?

A wire of length 2L and radius r is stretched between A and B without the application of any tension. If Y is the Young's modulus of the wire and it is stretched like ACB, then the tension in the wire will be

1. $\frac{{\mathrm{\pi r}}^2{\mathrm{Yd}}^3}{2L^2}$
2. $\frac{{\mathrm{\pi r}}^2{\mathrm{Yd}}^2}{2L^2}$
3. $\frac{{\pi }^{2}Y.2L^2}{d^2}$
4. $\frac{{\mathrm{\pi r}}^{2}Y.2L}{d}$

The diagram shows a force-extension graph for a rubber band. Consider the following statements:

I. It will be easier to compress this rubber than expand it.
II. The rubber does not return to its original length after it is stretched.
III. The rubber band will get heated if it is stretched and released.
Which of these can be deduced from the graph?
1. III only
2. II and III
3. I and III
4. I only

If the ratio of lengths, radii and Young's modulus of steel and brass wires shown in the figure are a, b and c respectively. The ratio between the increase in lengths of brass and steel wires would be :

1. $\frac{b^{2}a}{2c}$
2. $\frac{bc}{2a^2}$
3. $\frac{b{a}^2}{2c}$
4. $\frac{3b^{2}c}{2a}$

A uniform cylinder of length L and mass M having cross-sectional area A is suspended, with its length vertical, from a fixed point by a massless spring such that it is half-submerged in a liquid of density $\mathrm{\sigma }$ at equilibrium position. The extension ${\mathrm{x}}_0$ of the spring when it is in equilibrium is
1. $\frac{Mg}{k}$
2. $\frac{Mg}{k}\left(1-\frac{LA\sigma }{M}\right)$
3. $\frac{Mg}{k}\left(1-\frac{LA\sigma }{2M}\right)$
4. $\frac{Mg}{k}\left(1+\frac{LA\sigma }{M}\right)$

The stress versus strain graphs for wires of two materials A and B are as shown in the figure. If ${\mathrm{Y}}_{\mathrm{A}}$ $\mathrm{and}$ ${\mathrm{Y}}_{\mathrm{B}}$ are the Young's moduli of the materials, then:
            

The length of elastic string, obeying Hooke's law, is ${\mathrm{l}}_1$ metres when the tension 4N and ${\mathrm{l}}_2$ metres when the tension is 5N. The length in metres when the tension is 9N is
1. $5{\mathrm{l}}_1-4{\mathrm{l}}_2$
2. $5{\mathrm{l}}_2-4{\mathrm{l}}_1$
3. $9{\mathrm{l}}_1-8{\mathrm{l}}_2$
4. $9{\mathrm{l}}_2-8{\mathrm{l}}_1$

A thick rope of density $\mathrm{\rho }$ and length L is hung from a rigid support. The Young's modulus of the material of rope is Y. The increase in the length of the rope due to its own weight is :
1. $(1/4){\mathrm{\rho gL}}^2/\mathrm{Y}$
2. $(1/2){\mathrm{\rho gL}}^2/\mathrm{Y}$
3. ${\mathrm{\rho gL}}^2/\mathrm{Y}$
4. $\mathrm{\rho gL}/\mathrm{Y}$