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

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. \(4\times 10^{6}\) N/m²
2. \(2\times 10^{6}\) N/m²
3. \(2\times 10^{8}\) N/m²
4. \(8\times 10^{6}\) N/m²

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 length of elastic string, obeying Hooke's law is $l_1$ metres when the tension is 4N, and $l_2$ metres when the tension is 5N. The length in metres when the tension is 0 N will be-

1. $5l_1-4l_2$                                

2. $5l_2-4l_1$

3. $9l_1-8l_2$

4. $9l_2-8l_1$

Two wires are made of the same material and have the same volume. The first wire has a cross-sectional area A and the second wire has a cross-sectional area 3A. If the length of the first wire is increased by $∆\mathrm{l}$ on applying a force F, how much force is needed to stretch the second wire by the same amount?

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 'Δl'. Which of the following graph is a straight line?

1. $∆\mathrm{l}$ $\mathrm{vs}$ $\frac{1}{\mathrm{l}}$

2. $∆\mathrm{l}$ $\mathrm{vs}$ ${\mathrm{l}}^2$

3. $∆\mathrm{l}$ $\mathrm{vs}$ $\frac{1}{{\mathrm{l}}^2}$

4. $∆\mathrm{l}$ $\mathrm{vs}$ $\mathrm{l}$

Overall changes in volume and radius of a uniform cylindrical steel wire are 0.2% and 0.002% respectively when subjected to some suitable force. Longitudinal tensile stress acting on the wire is:
($\mathrm{Y}=2.0\times {10}^{11}$ ${\mathrm{Nm}}^{-2}$)

1.  $3.2\times {10}^{11}$ ${\mathrm{Nm}}^{-2}$

2.  $3.2\times {10}^7$ ${\mathrm{Nm}}^{-2}$

3.  $3.6\times {10}^9$ ${\mathrm{Nm}}^{-2}$

4.  3.9$\times {10}^8$ ${\mathrm{Nm}}^{-2}$

A 1000 kg lift is tied with metallic wires of maximum safe stress of 1.4 $\times$ 10⁸ N m^-2. If the maximum acceleration of the lift is 1.2 m s^-2, then the minimum diameter of the wire is:
1. 1 m 

2. 0.1 m

3. 0.01 m 

4. 0.001 m

A wire can sustain a weight of 10 kg before breaking. If the wire is cut into two equal parts, then each part can sustain a weight of:

A uniform cylinder rod of length L, cross-sectional area A and Young's modulus Y is acted upon by the forces, as shown in the figure. The elongation of the rod is:

1. $\frac{3FL}{5AY}$

2. $\frac{2FL}{5AY}$

3. $\frac{2FL}{8AY}$

4. $\frac{8FL}{3AY}$