The strain-stress curves of three wires of different materials are shown in the figure. \(P\), \(Q\) and \(R\) are the elastic limits of the wires. The figure shows that:
           

1.	Elasticity of wire \(P\) is maximum.
2.	Elasticity of wire \(Q\) is maximum.
3.	Tensile strength of \(R\) is maximum.
4.	None of the above is true.

The adjacent graph shows the extension $\left(∆l\right)$ of a wire of length 1m suspended from the top of a roof at one end with a load W connected to the other end. If the cross sectional area of the wire is ${10}^{-6}{m}^2$ calculate the young’s modulus of the material of the wire

1. $2\times {10}^{11}N/m^2$

2. $2\times {10}^{-11}N/m^2$

3. $3\times {10}^{-12}N/m^2$

4. $2\times {10}^{-13}N/m^2$

The diagram shows stress v/s strain curve for the materials A and B. From the curves we infer that

1. A is brittle but B is ductile  

2. A is ductile and B is brittle

3. Both A and B are ductile      

4. Both A and B are brittle

If the potential energy of a spring is V on stretching it by 2 cm, then its potential energy when it is stretched by 10 cm will be

1. V/25                                   

2. 5V

3. V/5                                    

4. 25V

A \(5~\text{m}\) long wire is fixed to the ceiling. A weight of \(10~\text{kg}\) is hung at the lower end and is \(1~\text{m}\) above the floor. The wire was elongated by \(1~\text{mm}.\) The energy stored in the wire due to stretching is:
1. zero                        
2. \(0.05~\text J\) 
3. \(100~\text J\)                          
4. \(500~\text J\)

If the force constant of a wire is \(K\), the work done in increasing the length of the wire by \(l\) is:
1. \(\frac{Kl}{2}\)
2. \(Kl\)
3. \(\frac{Kl^2}{2}\)
4. \(Kl^2\)

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

The stress versus strain graphs for wires of two materials A and B are as shown in the figure. If $Y_A$ and $Y_B$ are the Young ‘s modulii of the materials, then

1. $Y_B=2Y_A$

2. $Y_A=Y_B$

3. $Y_B=3Y_A$

4. $Y_A=3Y_B$

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 \(W_1\) is suspended from its lower end. If \(S\) is the area of cross-section of the wire, the stress in the wire at a height \(\frac{3L}{4}\) from its lower end is:
1. \(\frac{W_1}{S}\)
2. \(\frac{W_1+\left(\frac{W}{4}\right)}{S}\)
3. \(\frac{W_1+\left(\frac{3W}{4}\right)}{S}\)
4. \(\frac{W_1+W}{S}\)

Shearing stress causes a change in-

1.   Length                              

2.   Breadth

3.   Shape                               

4.   Volume