Deformation of Solids

A wire is extended by a tensile force so that its deformation is elastic.
What is meant by elastic deformation?

Options

A   The extension of the wire is proportional to the tensile force.
B   The extension of the wire is not proportional to the tensile force.
C   When the tensile force is removed, the wire does not return to its original length.
D   When the tensile force is removed, the wire returns to its original length.

A bolt is subjected to a tensile force, as shown.

The bolt has a circular cross-section. At end X, the diameter is $2d$. At end Y, the diameter is $d$.
What is the ratio

$$\frac{\text{stress at Y}}{\text{stress at X}}$$

Options

A   $0.25$
B   $0.50$
C   $2.0$
D   $4.0$

The graph shows the relationship between force acting on a compression spring and change in length of the spring.

One of these springs is placed in each corner of a horizontal square plate. The axis of each spring is in a vertical direction. These four springs support a total load of $160\text{ N}$.
What is the total elastic potential energy stored in the four springs?

Options

A   $0.048\text{ J}$
B   $0.19\text{ J}$
C   $0.38\text{ J}$
D   $0.77\text{ J}$

A student investigates a spring. The variation of the length of the spring with the force applied to the spring is shown.

What is the spring constant of the spring?

Options

A   $0.17\text{ N m}^{-1}$
B   $0.25\text{ N m}^{-1}$
C   $4.0\text{ N m}^{-1}$
D   $6.0\text{ N m}^{-1}$

The graph shows the variation with force of the extension of a wire.

The force is gradually increased to a maximum at Q and then gradually decreased to zero at R.

Which statement is correct?

Options

A   Along the line PQ, the wire obeys Hooke’s law.
B   Along the line RP, the spring constant is equal to $\dfrac{\text{extension}}{\text{force}}$.
C   The wire has elastic deformation at point Q.
D   The work done in stretching the wire to P is equal to $(\text{force} \times \text{extension})$ at point P.

A uniform metal wire of length $L$ and diameter $d$ has spring constant $k$.

What is the Young modulus of the metal?

Options

A   $\dfrac{\pi d^2}{4kL}$
B   $\dfrac{\pi d^2}{kL}$
C   $\dfrac{kL}{\pi d^2}$
D   $\dfrac{4kL}{\pi d^2}$

A student has a copper wire and a steel wire with equal lengths and cross-sectional areas.

The student hangs identical loads on the two wires.

The extensions of the two wires are different.

The student calculates the stress, strain and Young modulus of each wire.

Which row identifies with a tick ($\checkmark$) the calculated values that are equal for both wires?

Options

Two springs X and Y stretch elastically. The graphs show the variation with extension $x$ of the force $F$ applied to each spring.

Which statement is correct?

Options

A   When each spring is given the same extension, the energy stored in Y is $4$ times the energy stored in X.
B   When each spring is given the same extension, the energy stored in Y is $8$ times the energy stored in X.
C   When the same force is applied to each spring, the energy stored in Y is $4$ times the energy stored in X.
D   When the same force is applied to each spring, the energy stored in Y is $8$ times the energy stored in X.

Which phrase describes the strain at the elastic limit on a stress–strain graph?

Options

A   the maximum strain below which Hooke’s law is obeyed
B   the maximum strain below which the deformation is plastic
C   the minimum strain above which Hooke’s law is obeyed
D   the minimum strain above which the deformation is plastic

What are the units of stress, strain and the Young modulus?

Options