Q. No.A uniform wire of length \(l\) of weight \(w\) is suspended from the roof with weight of \(W\) at the other end. The stress in the wire at \(\dfrac{l}{3}\) distance from the top is \(\left(\dfrac{W}{A}+\dfrac{2}{\gamma} \dfrac{w}{A}\right)~\), where, \(A\) is the cross sectional area of the wire. The value of \(\gamma\) is:
1. \(2\)
2. \(3\)
3. \(5\)
4. \(6\)
1. \(2\)
2. \(3\)
3. \(5\)
4. \(6\)
Subtopic: Stress - Strain |
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Two wires as shown in the figure below, made of steel and have breaking stress of \(12 \times 10^8 ~\text{N/m}^2\) Area of cross-section of upper wire is \(0.008~\text{cm}^2\) and of lower wire is \(0.004~\text{cm}^2\). The maximum mass that can be added to pan without breaking any wire is: (in kg)
\(\left(\text { take } g=10 ~\text{m/s}^2\right)~\)
1. \(56\)
2. \(38\)
3. \(96\)
4. \(5.6\)
\(\left(\text { take } g=10 ~\text{m/s}^2\right)~\)
1. \(56\)
2. \(38\)
3. \(96\)
4. \(5.6\)
Subtopic: Stress - Strain |
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If the wire \(BC\) has Young's modulus of \(Y=2\times10^{11}~\text{N/m}^2\) and cross-section are \(5\times10^{-4}~\text{cm}^2.\) Then the strain in the wire \(BC\) is: (in units of \(10^{-4})\)
1. \(30\)
2. \(20\)
3. \(60\)
4. \(40\)
1. \(30\)
2. \(20\)
3. \(60\)
4. \(40\)
Subtopic: Stress - Strain |
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A rod is fixed at one end and other end is pulled with force \(F = 62.8\text{ kN},\) Young’s modulus of rod is \(2 × 10^{11} \text{ N/m}^2.\) If the radius of cross-section of rod is \(20\text{ mm}\) the strain produced in rod is:
1. \(2.5\times10^{-3}\)
2. \(2.5\times10^{-4}\)
3. \(2.0\times10^{-3}\)
4. \(2.0\times10^{-4}\)
1. \(2.5\times10^{-3}\)
2. \(2.5\times10^{-4}\)
3. \(2.0\times10^{-3}\)
4. \(2.0\times10^{-4}\)
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
(\(F=100\) 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
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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
1. \(15\) m/s
2. \(50\) m/s
3. \(25\) m/s
4. \(40\) m/s
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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. \(1.67\times10^{-4}~\text{m}^2\)
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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Two blocks of masses \(3~\text{kg}\) and \(5~\text{kg}\) are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is \(\frac{24}{\pi}\times10^2~\text{Nm}^{-2}.\) What is the minimum radius of the wire?
(take \(\text{g}=10~\text{ms}^{-2})\)
1. \(1250~\text{cm}\)
2. \(125~\text{cm}\)
3. \(12.5~\text{cm}\)
4. \(1.25~\text{cm}\)
(take \(\text{g}=10~\text{ms}^{-2})\)
1. \(1250~\text{cm}\)
2. \(125~\text{cm}\)
3. \(12.5~\text{cm}\)
4. \(1.25~\text{cm}\)
Subtopic: Stress - Strain |
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Wires \({W_1~\text{and}~W_2}\) are made of the same material having the breaking stress of \(1.25 \times 10^9~\text{N/m}^2.\) \({W_1~\text{and}~W_2}\) have cross-sectional area of \(8 \times 10^{-7} \text{m}^2 \text { and } 4 \times 10^{-7} \text{m}^2 \text {, }\) respectively. Masses of \({20~\text{kg and}~10~\text{kg}}\) hang from them as shown in the figure. The maximum mass that can be placed in the pan without breaking the wires is:\((\text{use } g=10~\text{m/s}^2 { ) }\)
1. \(10~\text{kg}\)
2. \(20~\text{kg}\)
3. \(30~\text{kg}\)
4. \(40~\text{kg}\)
1. \(10~\text{kg}\)
2. \(20~\text{kg}\)
3. \(30~\text{kg}\)
4. \(40~\text{kg}\)
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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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