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 graph shows the behaviour of a length of wire in the region for which the substance obeys Hook’s law. P and Q represent

1. P = applied force, Q = extension

2. P = extension, Q = applied force

3. P = extension, Q = stored elastic energy                       

4. P = stored elastic energy, Q = extension 

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

A 5 metre long wire is fixed to the ceiling. A weight of 10 kg is hung at the lower end and is 1 metre above the floor. The wire was elongated by 1 mm. The energy stored in the wire due to stretching is

1. Zero                                 

2. 0.05 joule

3. 100 joule                          

4. 500 joule

A wire is suspended by one end. At the other end a weight equivalent to 20 N force is applied. If the increase in length is 1.0 mm, the increase in energy of the wire will be

1. 0.01 J                               

2. 0.02 J

3. 0.04 J                               

4. 1.00 J

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. $Y_A=3Y_B$

When a force is applied on a wire of uniform cross-sectional area $3\times {10}^{-6}{m}^2$ and length 4m, the increase in length is 1 mm. Energy stored in it will be $\left(Y=2\times {10}^{11}N/m^2\right)$

1. 6250 J                               2. 0.177 J

3. 0.075 J                              4. 0.150 J

The diagram shows a force-extension graph for a rubber band. Consider the following statements

I. It will be easier to compress this rubber than expand it

II. Rubber does not return to its original length after it is stretched

III. The rubber band will get heated if it is stretched and released

 Which of these can be deduced from the graph?

1.   III only                              

2.   II and III

3.   I and III                            

4.   I only

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