The stress-strain curves are drawn for two different materials \(X\) and \(Y.\) It is observed that the ultimate strength point and the fracture point are close to each other for material \(X\) but are far apart for material \(Y.\) We can say that the materials \(X\) and \(Y\) are likely to be (respectively):

1.	ductile and brittle
2.	brittle and ductile
3.	brittle and plastic
4.	plastic and ductile

A vessel of \(1\times 10^{-3}\) m³ volume contains oil. When a pressure of \(1.2 \times10^5\) N/m² is applied on it, then volume decreases by \(0.3 \times 10^{-6}\) m³. The bulk modulus of oil is:

A wire of negligible mass and length 2 m is stretched by hanging a 20 kg load to its lower end keeping its upper end fixed. If work done in stretching the wire is 50 J, then the strain produced in the wire will be:

1. 0.5

2. 0.1

3. 0.4

4. 0.25

The length of an elastic string is \(a\) metre when the longitudinal tension is \(4\) N and \(b\) metre when the longitudinal tension is \(5\) N. The length of the string in metre when the longitudinal tension is \(9\) N will be:

The compressibility of water is $4\times {10}^{-5}$ per unit atmospheric pressure. The decrease in volume of 100 cubic centimeter of water under a pressure of 100 atmosphere will be:

1. 0.4 cc         

2. $4\times {10}^{-5}cc$

3. 0.025 cc       

4. 0.004 cc 

A uniform cube is subjected to volume compression. If each side is decreased by 1%, then bulk strain is:

A ball falling into a lake of depth 200 m shows a 0.1% decrease in its volume at the bottom. What is the bulk modulus of the material of the ball?

1. $19.6\times {10}^{8}N/m^2$               

2. $19.6\times {10}^{-10}N/m^2$

3. $19.6\times {10}^{10}N/m^2$               

4. $19.6\times {10}^{-8}N/m^2$

The ratio of Young's modulus of the material of two wires is 2 : 3. If the same stress is applied on both, then the ratio of elastic energy per unit volume will be:

1. 3 : 2                                   

2. 2 : 3

3. 3 : 4                                   

4. 4 : 3

If \(\mathrm{E}\) is the energy stored per unit volume in a wire having \(\mathrm{Y}\) as Young's modulus of the material, then the stress applied is:
1. $\sqrt{2\mathrm{EY}}$

2. $2\sqrt{\mathrm{EY}}$

3. $\frac{1}{2}\sqrt{\mathrm{EY}}$

4. $\frac{3}{2}\sqrt{\mathrm{EY}}$

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: