To break a wire, a force of \(10^6~\text{N/m}^{2}\) is required. If the density of the material is \(3\times 10^{3}~\text{kg/m}^3,\) then the length of the wire which will break by its own weight will be:
1. \(34~\text m\) 
2. \(30~\text m\) 
3. \(300~\text m\) 
4. \(3~\text m\) 

One end of a uniform wire of length \(L\) and of weight \(W\) is attached rigidly to a point in the roof and a weight \(W_1\) is suspended from its lower end. If \(A\) is the area of the cross-section of the wire, the stress in the wire at a height \(\frac{3L}{4}\) from its lower end is:
1. \(\frac{W+W_1}{A}\)
2. \(\frac{4W+W_1}{3A}\)
3. \(\frac{3W+W_1}{4A}\)
4. \(\frac{\frac{3}{4}W+W_1}{A}\)

The following four wires (length \(L\) and diameter \(D\)) are made of the same material. Which of these will have the largest extension when the same tension is applied?

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

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 for an incompressible liquid is:
1. zero
2. unity
3. infinity
4. between \(0\) and \(1\)

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. \(\frac{1}{2}Mgl\)

lf \(\rho\) is the density of the material of a wire and \(\sigma\) is the breaking stress, the greatest length of the wire that can hang freely without breaking is:
1. \(\dfrac{2}{\rho g}\)

2. \(\dfrac{\rho}{\sigma g}\)

3. \(\dfrac{\rho g}{2 \sigma}\)

4. \(\dfrac{\sigma}{\rho g}\)