Deformation of Solids

Which of the following correctly defines the terms stress, strain and Young modulus?

• A

• B

• C

• D

A wire is stretched by 8 mm when a load of 60 N is applied. What will be the extension of a wire of the same material having four times the cross-sectional area and twice the original length, when the same load is applied?

• 2 mm

• 4 mm

• 8 mm

• 16 mm

The tension in a spring of natural length I₀ is first increased from zero to T₁, causing the length to increase to I₁. The tension is then reduced to T₂, causing the length to decrease to T₂ (as shown).

Which area of the graph represents the work done by the spring during this reduction in length?

• MLP

• MNQP

• MNSR

• MPLU

Two springs P and Q both obey Hooke’s law. They have spring constants 2k and k respectively. The springs are stretched, separately, by a force that is gradually increased from zero up to a certain maximum value, the same for each spring. The work done in stretching spring P is W_P, and the work done in stretching spring Q is W_Q. How is W_P related to W_Q?

• W_{P = 1/4} W_Q

• W_{P = 1/2} W_Q

• W_{P = 2}W_Q

• W_{P = 4}W_Q

A number of similar springs, each having the same spring constant, are joined in three arrangements X, Y and Z. The same load is applied to each. What is the order of increasing extension for these arrangements?

• A

• B

• C

• D

What is plastic deformation?

• Plastic deformation occurs when strain is not proportional to stress but when the load is removed the material returns to its original length.

• Plastic deformation occurs if, when the load is removed, the material contracts but a permanent stretching has occurred.

• Plastic deformation occurs until the extension is no longer proportional to the load.

• Plastic deformation occurs when the material extends so that strain is directly proportional to stress.

The graph shows how the length of a particular rubber cord varies as force is applied. What is the maximum strain energy in this deformed rubber cord?

• 2.5 J

• 5.0 J

• 7.5 J

• 10 J

The Young modulus of steel is determined using a length of steel wire and is found to have the value E. Another experiment is carried out using a wire of the same steel, but of twice the length and half the diameter. What value is obtained for the Young modulus in the second experiment?

• 4E
• E/2
• 2E
• E

A wire is fixed at one end and is extended by a force F₁ acting on the other end. This causes the wire to have an elastic potential energy of 0.15 J. The force applied to the wire is now changed to a force F₂. This causes the wire to have a new elastic potential energy of 0.60 J. The wire obeys Hooke’s law. What is the relationship between F₁ and F₂?

• F₁ = 2F₂

• F₁ = 4F₂

• 2F₁ = F₂

• 4F₁ = F₂

When a force of 0.80 N is applied to a spring, the length of the spring is 90 mm. When a force of 1.30 N is applied to the same spring, its length is 115 mm. The spring obeys Hooke’s law. What is the spring constant of the spring?

• 8.9 N m^–1

• 10 N m^–1

• 11 N m^–1

• 20 N m^–1