The maximum load a wire can withstand without breaking when its length is reduced to half of its original length, will:
1. be doubled
2. be halved
3. be four times
4. remain the same
A mild steel wire of length \(2L\) and cross-sectional area \(A\) is stretched, well within the elastic limit, horizontally between two pillars (figure). A mass \(m\) is suspended from the mid-point of the wire. Strain in the wire is:
1. | \( \dfrac{x^2}{2 L^2} \) | 2. | \(\dfrac{x}{\mathrm{~L}} \) |
3. | \(\dfrac{x^2}{L}\) | 4. | \(\dfrac{x^2}{2L}\) |
Hooke's law is applicable for:
1. | elastic materials only | 2. | plastic materials only |
3. | elastomers only | 4. | all of these |
How much should the pressure on a litre of water be changed to compress it by \(0.10 \%?\)
(Given Bulk modulus of water, \(\beta=2.2\times 10^9~\text{N-m}^2\))
1. \(4.8 \times 10^6~\text{N/m}^2\)
2. \(2.2 \times 10^6~\text{N/m}^2\)
3. \(5.1 \times 10^6~\text{N/m}^2\)
4. \(3.3 \times 10^6~\text{N/m}^2\)
The volume contraction of a solid copper cube, \(10~\text{cm}\) on an edge, when subjected to a hydraulic pressure of \(7.0\times10^6~\text{Pa}\) is:
(Bulk modulus of copper is \(140 \times10^{9}~\text{Pa}.\))
1. \( 3.1 \times 10^{-2} ~\text{m}^3 \)
2. \(9.1 \times 10^{-3} ~\text{cm}^3 \)
3. \(5.0 \times 10^{-2} ~\text{cm}^3 \)
4. \(7.9 \times 10^{-2} ~\text{cm}^3 \)
Two wires of diameter \(0.25\) cm, one made of steel and the other made of brass are loaded, as shown in the figure. The unloaded length of the steel wire is \(1.5\) m and that of the brass wire is \(1.0\) m. The elongation of the steel wire will be:
(Given that Young's modulus of the steel, \(Y_S=2 \times 10^{11}\) Pa and Young's modulus of brass, \(Y_B=1 \times 10^{11}\) Pa)
1. | \(1.5 \times 10^{-4}\) m | 2. | \(0.5 \times 10^{-4}\) m |
3. | \(3.5 \times 10^{-4}\) m | 4. | \(2.5 \times 10^{-4}\) m |
The edge of an aluminum cube is \(10~\text{cm}\) long. One face of the cube is firmly fixed to a vertical wall. A mass of \(100~\text{kg}\) is then attached to the opposite face of the cube. The shear modulus of aluminum is \(25~\text{GPa}.\) What is the vertical deflection of this face?
1. \(4.86 \times10^{-6}~\text m\)
2. \(3.92 \times 10^{-7}~\text m\)
3. \(3.01 \times10^{-6}~\text m\)
4. \(6.36 \times10^{-7}~\text m\)
The stress-strain graphs for materials \(A\) and \(B\) are shown in the figure. The strength of the material \(A\) is:
(The graphs are drawn to the same scale)
1. | greater than material \(B\) |
2. | equal to material \(B\) |
3. | less than material \(B\) |
4. | insufficient data |
The figure shows the strain-stress curve for a given material. What is Young’s modulus for this material?
1. \(7.5\times10^{11}~\text{Nm}^{-2}\)
2. \(7.5\times10^{10}~\text{Nm}^{-2}\)
3. \(7.5\times10^{9}~\text{Nm}^{-2}\)
4. \(7.5\times10^{-10}~\text{Nm}^{-2}\)