A man transforms into a giant such that all his linear dimensions become \(9\) times their original values. Assuming his density remains unchanged, the stress on his legs changes by a factor of:

1. \(9\) 2. \(\dfrac{1}{9}\)
3. \(81\) 4. \(\dfrac{1}{81}\)
Subtopic:  Stress - Strain |
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A steel wire having a radius of \(2.0\) mm, carrying a load of \(4\) kg, is hanging from a ceiling. Given that \(g=3.1\pi~\text{m/s}^{2}\)what will be the tensile stress that would be developed in the wire?
1. \(5.2\times10^{6}~\text{N/m}^{2}\) 2. \(6.2\times10^{6}~\text{N/m}^{2}\)
3. \(4.8\times10^{6}~\text{N/m}^{2}\) 4. \(3.1\times10^{6}~\text{N/m}^{2}\)
Subtopic:  Stress - Strain |
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In an experiment, brass and steel wires of length \(1~\text{m}\) each with areas of cross section \(1~\text{mm}^2\) are used. The wires are connected in series and one end of the combined wire is connected to a rigid support and other end is subjected to elongation. The stress required to produce a net elongation of \(0.2~\text{mm}\) is, [Given, the Young's Modulus for steel and brass are, respectively, \(120 \times 10^9 ~\text{N/m}^2\) and \(60 \times 10^9 ~\text{N/m}^2\)]
1. \( 4.0 \times 10^6 ~\text{N/m}^2\)
2. \( 1.2 \times 10^6~\text{N/m}^2\)
3. \( 1.8 \times 10^6~\text{N/m}^2\)
4. \(8 \times 10^6~\text{N/m}^2\)

Subtopic:  Stress - Strain |
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The elastic limit of brass is 400 MPa. What should be the minimum diameter of a brass rod if it is to support a 400\(\pi \) N load without exceeding its elastic limit?
1. 1 mm
2. 1.5 mm
3. 2 mm
4. 2.5 mm

Subtopic:  Stress - Strain |
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A body of mass \(m = 10 ~\text{kg}\) is attached to one end of a wire of length \(0.3 ~\text{m}.\) The maximum angular speed (in \(\text{rad}~\text s^{–1}\)) with which it can be rotated about its other end in the space station is:
(Breaking stress of wire = \(4.8 \times 10^7 ~\text{Nm}^{-2}\) and area of cross-section of the wire = \(10^{-2}~ \text {cm}^{-2}\))
1. \(4~\text{rad s}^{-1}\)
2. \(6~\text{rad s}^{-1}\)
3. \(8~\text{rad s}^{-1}\)
4. \(9~\text{rad s}^{-1}\)
Subtopic:  Stress - Strain |
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A uniform metallic wire is elongated by \(0.04\) m when subjected to a linear force \(F\). The elongation, if its length and diameter are doubled and subjected to the same force will be:

1. \(1\) cm 2. \(2 \) cm
3. \(3\) cm 4. \(6\) cm
Subtopic:  Stress - Strain |
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The area of cross-section of the rope used to lift a load by a crane is \(2.5\times10^{-4}~\text{m}^2.\) The maximum lifting capacity of the crane is \(10~\text{metric tons}.\) To increase the lifting capacity of the crane to \(25~\text{metric tons},\) the required area of the cross-section of the rope should be: (Take \(g=10~\text{ms}^{-2}\) )
1. \(6.25\times10^{-4}~\text{m}^2\) 
2. \(10\times10^{-4}~\text{m}^2\)
3. \(1\times10^{-4}~\text{m}^2\) 
4. \(1.67\times10^{-4}~\text{m}^2\) 
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A metal wire of length \(0.5\) m and cross-sectional area \(10^{-4}\) m2 has breaking stress \(5\times10^{8}\) Nm–2. A block of \(10\) kg is attached at one end of the string and is rotating in a horizontal circle. The maximum linear velocity of the block will be:
1. \(15\) m/s
2. \(50\) m/s
3. \(25\) m/s
4. \(40\) m/s
Subtopic:  Stress - Strain |
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A wire of length \(l,\) cross-sectional area \(A\) is pulled as shown. \(Y\) is Young’s modulus of wire. The elongation in wire is:
(\(F=100\) N, \(A=10\) cm2\(l=1\) m, \(Y=5\times10^{10}\) N/m2)

   
1. \(10^{-6}\) m
2. \(10^{-5}\) m
3. \(2\times10^{-6}\) m
4. \(2\times10^{-5}\) m
Subtopic:  Stress - Strain |
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A rod is fixed at one end and other end is pulled with force F = 62.8 kN, Young’s modulus of rod is 2 × 1011 N/m2. If the radius of cross-section of rod is 20 mm the strain produced in rod is

1. 2.5 × 10–3
2. 2.5 × 10–4
3. 2 × 10–3
4. 2 × 10–4
Subtopic:  Stress - Strain |
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