A wire of length \(L,\) area of cross section \(A\) is hanging from a fixed support. The length of the wire changes to \({L}_1\) when mass \(M\) is suspended from its free end. The expression for Young's modulus is:

1.	\(\dfrac{{Mg(L}_1-{L)}}{{AL}}\)	2.	\(\dfrac{{MgL}}{{AL}_1}\)
3.	\(\dfrac{{MgL}}{{A(L}_1-{L})}\)	4.	\(\dfrac{{MgL}_1}{{AL}}\)

The stress versus strain graph is shown for two wires. If \(Y_1\) and \(Y_2\) are Young modulus of wire \(A\) and \(B\) respectively, then the correct option is:

The stress-strain graphs for materials \(A\) and \(B\) are shown in the figure. Young’s modulus of material \(A\) is:
(the graphs are drawn to the same scale)

The edge of an aluminum cube is \(10~\text{cm}\) long. One face of the cube is firmly fixed to a vertical wall. A mass of \(100~\text{kg}\)  is then attached to the opposite face of the cube. The shear modulus of aluminum is \(25~\text{GPa}.\) What is the vertical deflection of this face?
1. \(4.86\times 10^{-6}~\text{m}\)
2. \(3.92\times 10^{-7}~\text{m}\)
3. \(3.01\times 10^{-7}~\text{m}\)
4. \(6.36\times 10^{-7}~\text{m}\)

The volume contraction of a solid copper cube, \(10~\text{cm}\) on an edge, when subjected to a hydraulic pressure of \(7.0\times10^6~\text{Pa}\) is:
(Bulk modulus of copper is \(140 \times10^{9}~\text{Pa}.\))
1. \( 3.1 \times 10^{-2} ~\text{m}^3 \)
2. \(9.1 \times 10^{-3} ~\text{cm}^3 \)
3. \(5.0 \times 10^{-2} ~\text{cm}^3 \)
4. \(7.9 \times 10^{-2} ~\text{cm}^3 \)$$

Hooke's law is applicable for:

If two different types of rubber are found to have stress-strain curves as shown, then:
                   

The stress-strain graphs for two materials \(A\) and \(B\) are shown in the figure. The graphs are drawn to the same scale. Select the correct statement:

1. material \(A\) has a greater Young's Modulus.
2. material \(A\) is ductile. 
3. material \(B\) is brittle.
4. all of these.

On withdrawing the external applied force on bodies within the elastic limit, the body: