A mild steel wire of length \(\mathrm{2L}\) 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. \( \frac{x^2}{2 L^2} \)
2. \(\frac{x}{\mathrm{~L}} \)
3. \(\frac{x^2}{L}\)
4. \(\frac{x^2}{2L}\)

Subtopic:  Stress - Strain |
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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

Subtopic:  Stress - Strain |
 60%
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The modulus of rigidity of the ideal liquid is:

1. infinity
2. zero
3. unity
4. some finite small non-zero constant value
Subtopic:  Shear and bulk modulus |
 66%
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Hooke's law is applicable for:

1. elastic materials only 2. plastic materials only
3. elastomers only 4. all of these

Subtopic:  Hooke's Law |
 68%
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How much should the pressure on a litre of water be changed to compress it by \(0.10 \%?\)
(Given Bulk modulus of water, \(B=2.2\times 10^9\) N-m-2)
1. \(4.8 \times 10^6\) N/m2 
2. \(2.2 \times 10^6\) N/m2 
3. \(5.1 \times 10^6\) N/m2 
4. \(3.3 \times 10^6\) N/m2 

Subtopic:  Shear and bulk modulus |
 88%
From NCERT
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The volume contraction of a solid copper cube, 10 cm on an edge, when subjected to a hydraulic pressure of \(7.0\times10^6\) Pa is: (Bulk modulus of copper is 140×109 Pa.)
1. \( 3.1 \times 10^{-2} \mathrm{~m}^3 \)
2. \(9.1 \times 10^{-3} \mathrm{~cm}^3 \)
3. \(5.0 \times 10^{-2} \mathrm{~cm}^3 \)
4. \(7.9 \times 10^{-2} \mathrm{~cm}^3\)

Subtopic:  Shear and bulk modulus |
 81%
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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
Subtopic:  Young's modulus |
 55%
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The edge of an aluminium cube is \(10\) cm long. One face of the cube is firmly fixed to a vertical wall. A mass of \(100\) kg is then attached to the opposite face of the cube. The shear modulus of aluminium is \(25\) GPa. What is the vertical deflection of this face?
1. \(4.86 \times10^{-6}\) m
2. \(3.92 \times 10^{-7}\) m
3. \(3.01 \times10^{-6}\) m
4. \(6.36 \times10^{-7}\) m

Subtopic:  Shear and bulk modulus |
 66%
From NCERT
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The stress-strain graphs for materials \(A\) and \(B\) are shown in the figure. Strength of 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

Subtopic:  Stress - Strain Curve |
 72%
From NCERT
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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. \(7.5\times10^{-10}~\text{Nm}^{-2}\)

Subtopic:  Stress - Strain Curve |
 79%
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