Which of the following relation is true?

1.  $3\mathrm{Y} = \mathrm{k}\left(1 - \mathrm{\sigma }\right)$

2.  $\mathrm{K} = \frac{9\mathrm{\eta Y}}{\mathrm{Y} + \mathrm{\eta }}$

3.  $\mathrm{\sigma } = \left(6\mathrm{K} + \mathrm{\eta }\right)\mathrm{Y}$

4.  $\mathrm{\sigma } = \frac{0.5 \mathrm{Y} - \mathrm{\eta }}{\mathrm{\eta }}$

Practically range of Possion’s ratio $\mathrm{\sigma }$ is

1. 0.5 to 1

2. –1 to 0.5

3. 0 to 0.5

4. –0.5 to 0

The Poisson ratio cannot have value

(1) 0.7

(2) 0.2

(3) 0.1

(4) 0.5

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):

A cylindrical wire of radius 1 mm, length 1m, Young's modulus $=2\times {10}^{11} \mathrm{N}/{\mathrm{m}}^2$, poisson's ratio $\mathrm{\mu }=\mathrm{\pi }/10$ is stretched by a force of 100 N. Its radius will become?

1.  0.99998 mm

2.  0.99999 mm

3.  0.99997 mm

4.  0.99995 mm

When a block of mass \(M\) is suspended by a long wire of length \(L,\) the length of the wire becomes \((L+l).\) The elastic potential energy stored in the extended wire is:
1. \(\frac{1}{2}MgL\)
2. \(Mgl\)
3. \(MgL\)
4. \(\frac{1}{2}Mgl\)

If Young modulus (Y) equal to bulk modulus (B). Then the Poisson ratio is :

1. $\frac{1}{3}$

2. $\frac{2}{3}$

3. $\frac{1}{2}$

4. $\frac{1}{4}$

The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied?

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 \(\Delta l\) on applying a force \(F\), how much force is needed to stretch the second wire by the same amount?