The compressibility of water is \(4\times 10^{-5}\) per unit atmospheric pressure. The decrease in volume of \(100\) cubic centimeter of water under a pressure of \(100\) atmosphere will be:
1. \(0.4~\text{cc}\)
2. \(4\times 10^{-5}~\text{cc}\)
3. \(0.025~\text{cc}\)
4. \(0.004~\text{cc}\)

A uniform cube is subjected to volume compression. If each side is decreased by \(1\%\), then bulk strain is:

A ball falling into a lake of depth \(200~\text{m}\) shows a \(0.1\%\) decrease in its volume at the bottom. What is the bulk modulus of the material of the ball?
1. \(19.6\times 10^{8}~\text{N/m}^2\)
2. \(19.6\times 10^{-10}~\text{N/m}^2\)
3. \(19.6\times 10^{10}~\text{N/m}^2\)
4. \(19.6\times 10^{-8}~\text{N/m}^2\)

The ratio of Young's modulus of the material of two wires is \(2:3\). If the same stress is applied on both, then the ratio of elastic energy per unit volume will be:
1. \(3:2\)
2. \(2:3\)
3. \(3:4\)
4. \(4:3\)

If \(E\) is the energy stored per unit volume in a wire having \(Y\) as Young's modulus of the material, then the stress applied is:
1. \(\sqrt{2EY}\)
2. \(2\sqrt{EY}\)
3. \(\frac{1}{2}\sqrt{EY}\)
4. \(\frac{3}{2}\sqrt{EY}\)

The length of an elastic string is \(a\) metre when the longitudinal tension is \(4\) N and \(b\) metre when the longitudinal tension is \(5\) N. The length of the string in metre when the longitudinal tension is \(9\) N will be:

A wire of negligible mass and length 2 m is stretched by hanging a 20 kg load to its lower end keeping its upper end fixed. If work done in stretching the wire is 50 J, then the strain produced in the wire will be:

1. 0.5

2. 0.1

3. 0.4

4. 0.25

The breaking stress of a wire depends on:

The increase in the length of a wire on stretching is \(0.04\)%. If Poisson's ratio for the material of wire is \(0.5,\) then the diameter of the wire will:

A uniform wire of length \(3\) m and mass \(10\) kg is suspended vertically from one end and loaded at another end by a block of mass \(10\) kg. The radius of the cross-section of the wire is \(0.1\) m. The stress in the middle of the wire is: (Take \(g=10\) ms^-2)