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:

1.	\(a-b\)	2.	\(5b-4a\)
3.	\(2b-\frac{1}{4}a\)	4.	\(4a-3b\)

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 m shows a 0.1% decrease in its volume at the bottom. What is the bulk modulus of the material of the ball?

1. $19.6\times {10}^{8}N/m^2$               

2. $19.6\times {10}^{-10}N/m^2$

3. $19.6\times {10}^{10}N/m^2$               

4. $19.6\times {10}^{-8}N/m^2$

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

2. $2\sqrt{\mathrm{EY}}$

3. $\frac{1}{2}\sqrt{\mathrm{EY}}$

4. $\frac{3}{2}\sqrt{\mathrm{EY}}$

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)

The elongation (x) of a steel wire varies with the elongating force (F) according to the graph: (within elastic limit)

1.		2.
3.		4.

The stress-strain curve for two materials A and B are as shown in the figure. Select the correct statement:

The Young's modulus of a wire is numerically equal to the stress at a point when:

A metallic rope of diameter \(1~ \text{mm}\) breaks at \(10 ~\text{N}\) force. If the wire of the same material has a diameter of \(2~\text{mm}\), then the breaking force is: