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. \(Kl^2\)

When strain is produced in a body within elastic limit, its internal energy:
1. Remains constant                  
2. Decreases
3. Increases                               
4. None of the above

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. $Y_A=3Y_B$

If a spring extends by x on loading, then the energy stored by the spring is (if T is tension in the spring and k is spring constant)

1. $\frac{T^2}{2x}$                                     

2. $\frac{T^2}{2k}$

3. $\frac{2x}{T^2}$                                     

4. $\frac{2T^2}{k}$

A stretched rubber has:

1. increased kinetic energy.

2. increased potential energy.

3. decreased kinetic energy.

4. decreased potential energy.

When load of 5kg is hung on a wire then extension of 3m takes place, then work done will be

1. 75 joule                            

2. 60 joule

3. 50 joule                             

4. 100 joule

Two wires of the same diameter of the same material having the length \(l\) and \(2l.\) If the force \(F\) is applied on each, the ratio of the work done in the two wires will be:
1. \(1 : 2       \)
2. \(1 : 4\)
3. \(2 : 1           \)
4. \(1 : 1\)