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

1.	\(\dfrac{{Mg(L}_1-{L)}}{{AL}}\)	2.	\(\dfrac{{MgL}}{{AL}_1}\)
3.	\(\dfrac{{MgL}}{{A(L}_1-{L})}\)	4.	\(\dfrac{{MgL}_1}{{AL}}\)

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):

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. \(\frac{1}{2}MgL\)
2. \(Mgl\)
3. \(MgL\)
4. \(\frac{1}{2}Mgl\)

Copper of fixed volume \(V\) is drawn into a wire of length \(l.\) When this wire is subjected to a constant force \(F,\) the extension produced in the wire is \(\Delta l.\) Which of the following graphs is a straight line?
1. \(\Delta l ~\text{vs}~\dfrac{1}{l}\)
2. \(\Delta l ~\text{vs}~l^2\)
3. \(\Delta l ~\text{vs}~\dfrac{1}{l^2}\)
4. \(\Delta l ~\text{vs}~l\)

Young’s modulus of steel is twice that of brass. Two wires of the same length and of the same area of cross-section, one of steel and another of brass, are suspended from the same roof. If we want the lower ends of the wires to be at the same level, then the weights added to the steel and brass wires must be in the ratio of:
1. \(1:2\)
2. \(2:1\)
3. \(4:1\)
4. \(1:1\)

The bulk modulus of a spherical object is \(B.\) If it is subjected to uniform pressure \(P,\) the fractional decrease in radius is:

Two wires are made of the same material and have the same volume. The first wire has a cross-sectional area \(A\) and the second wire has a cross-sectional area \(3A\). If the length of the first wire is increased by \(\Delta l\) on applying a force \(F\), how much force is needed to stretch the second wire by the same amount?

The following four wires are made of the same material. Which of them will have the largest extension when the same tension is applied?

(1) Length=50 cm, diameter=0.5 mm 

(2) Length=100 cm, diameter=1 mm 

(3) Length=200 cm, diameter=2 mm 

(4) Length=300 cm, diameter=3 mm