Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A):
The stretching of a spring is determined by the shear modulus of the material of the spring.
Reason (R):
A coil spring of copper has more tensile strength than a steel spring of the same dimensions.
In light of the above statements, choose the most appropriate answer from the options given below:
1. (A) is false but (R) is true
2. Both (A) and (R) are true and (R) is the correct explanation of (A)
3. Both (A) and (R) are true and (R) is not the correct explanation of (A)
4. (A) is true but (R) is false

A wire of length L, area of cross section A is hanging from a fixed support. The length of the wire changes to ${\mathrm{L}}_1$ when mass M is suspended from its free end. The expression for Young's modulus is:

1. $\frac{\mathrm{Mg}({\mathrm{L}}_1-\mathrm{L})}{\mathrm{AL}}$

2. $\frac{\mathrm{MgL}}{{\mathrm{AL}}_1}$

3. $\frac{\mathrm{MgL}}{\mathrm{A}({\mathrm{L}}_1-\mathrm{L})}$

4. $\frac{{\mathrm{MgL}}_1}{\mathrm{AL}}$

The stress-strain curves are drawn for two different materials \(X\) and \(Y.\) It is observed that the ultimate strength point and the fracture point are close to each other for material \(X\) but are far apart for material \(Y.\) We can say that the materials \(X\) and \(Y\) are likely to be (respectively):
1. ductile and brittle
2. brittle and ductile
3. brittle and plastic
4. plastic and ductile

When a block of mass M is suspended by a long wire of length L, the length of the wire becomes (L+l). The elastic potential energy stored in the extended wire is:

1. $\frac{1}{2}\mathrm{MgL}$

2. Mgl

3. MgL

4. $\frac{1}{2}\mathrm{Mgl}$