To break a wire, a force of ${10}^6$ $N/m^2$ is required. If the density of the material is $3\times {10}^3$ $kg/m^3$, then the length of the wire which will break by its own weight will be:

1. 34 m

2. 30 m

3. 300 m

4. 3 m

The bulk modulus of water is $2\times {10}^9$ $\mathrm{N}/{\mathrm{m}}^2$. The increase in pressure required to decrease the volume of water sample by \(0.1\)% is:
1. \(4 \times 10^6 \mathrm{~N} / \mathrm{m}^2 \)
2. \(2 \times 10^{\mathrm{6}}~ \mathrm{N} / \mathrm{m}^2 \)
3. \(2 \times 10^{\mathrm{8}}~ \mathrm{N} / \mathrm{m}^2 \)
4. \(8 \times 10^{\mathrm{6}}~ \mathrm{N} / \mathrm{m}^2 \)

One end of a uniform wire of length L and of weight W is attached rigidly to a point in the roof and a weight W₁ is suspended from its lower end. If A is the area of cross-section of the wire , the stress in the wire at a height 3L/4 from its lower end is:

1.  $\frac{\mathrm{W}+{\mathrm{W}}_1}{\mathrm{A}}$

2.  $\frac{4\mathrm{W}+{\mathrm{W}}_1}{3\mathrm{A}}$

3.  $\frac{3\mathrm{W}+{\mathrm{W}}_1}{4\mathrm{A}}$

4.  $\frac{{\displaystyle \frac{3}{4}}\mathrm{W}+{\mathrm{W}}_1}{\mathrm{A}}$

Copper of fixed volume \(V\) is drawn into a wire of length \(l.\) When this wire is subjected to a constant force \(F,\) the extension produced in the wire is \(\Delta l.\) Which of the following graphs is a straight line?
1. \(\Delta l ~\text{vs}~\frac{1}{l}\)
2. \(\Delta l ~\text{vs}~l^2\)
3. \(\Delta l ~\text{vs}~\frac{1}{l^2}\)
4. \(\Delta l ~\text{vs}~l\)

If the ratio of lengths, radii and Young's modulus of steel and brass wires in the figure are \(a,\) \(b\) and \(c\) respectively, then the corresponding ratio of increase in their lengths will be:

1. $\frac{2a^{2}c}{b}$

2. $\frac{3a}{2b^{2}c}$

3. $\frac{2ac}{b^2}$

4. $\frac{3c}{2a{b}^2}$

A material has Poisson's ratio of 0.5. If a uniform rod made of it suffers a longitudinal strain of $2\times {10}^{-3}$, what is the percentage increase in volume?

1.  2%

2.  4%

3.  0%

4.  5%

lf $\mathrm{\rho }$ is the density of the material of a wire and $\sigma$ is the breaking stress, the greatest length of the wire that can hang freely without breaking is:

1.$\frac{2}{\mathrm{\rho g}}$

2. $\frac{\mathrm{\rho }}{\mathrm{\sigma g}}$

3.$\frac{\mathrm{\rho g}}{2\mathrm{\sigma }}$

4. $\frac{\mathrm{\sigma }}{\mathrm{\rho g}}$

The work done per unit volume to stretch the length of a wire by 1%  with a constant cross-sectional area will be: $\left[Y=9\times {10}^{11}N/m^2\right]$

1. $9\times {10}^{11}$ $J$

2. $4.5\times {10}^{7}J$

3. $9\times {10}^{7}J$

4. $4.5\times {10}^{11}$ $J$

A wire of length \(L\) and cross-sectional area \(A\) is made of a material of Young's modulus \(Y.\) It is stretched by an amount \(x.\) The work done is:
1. $\frac{YxA}{2L}$

2. $\frac{Y{x}^{2}A}{L}$

3. $\frac{Y{x}^{2}A}{2L}$

4. $\frac{2Y{x}^{2}A}{L}$

The Young's modulus of a wire is Y.  If the energy per unit volume is E, then the strain will be:

1. $\sqrt{\frac{2E}{Y}}$                                         

2. $\sqrt{2EY}$

3. $EY$                                             

4. $\frac{E}{Y}$