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Q. No.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. \(1.67\times10^{-4}~\text{m}^2\)
Subtopic: Stress - Strain |
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A uniform heavy rod of mass \(20\) kg, cross-sectional area of \(0.4\) m2 and length of \(20\) m is hanging from a fixed support. Neglecting the lateral contraction, the elongation in the rod due to its own weight is:
(Given: Young’s modulus \(Y=2\times 10^{11}\) N-m–2 and \(g=10~\text{ms}^{–2 }\) )
1. \(12\times 10^{-9}\) m
2. \(30\times 10^{-9}\) m
3. \(25\times 10^{-9}\) m
4. \(35\times 10^{-9}\) m
(Given: Young’s modulus \(Y=2\times 10^{11}\) N-m–2 and \(g=10~\text{ms}^{–2 }\) )
1. \(12\times 10^{-9}\) m
2. \(30\times 10^{-9}\) m
3. \(25\times 10^{-9}\) m
4. \(35\times 10^{-9}\) m
Subtopic: Young's modulus |
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A square aluminium (shear modulus is \(25\times10^{9}~\text{Nm}^{-2}\)) slab of side \(60~\text{cm}\) and thickness of \(15~\text{cm}\) is subjected to a shearing force (on its narrow face) of \(18.0\times10^{4}~\text {N}.\) The lower edge is riveted to the floor. The displacement of the upper edge is:
1. \(30~\mu \text m\)
2. \(48~\mu \text m\)
3. \(16~\mu \text m\)
4. \(64~\mu \text m\)
1. \(30~\mu \text m\)
2. \(48~\mu \text m\)
3. \(16~\mu \text m\)
4. \(64~\mu \text m\)
Subtopic: Shear and bulk modulus |
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Level 2: 60%+
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A steel wire of length \(3.2\) m (\(Y_S=2.0 \times 10^{11}\) N m–2 ) and a copper wire of length \(4.4\) m (\(Y_C=1.1 \times 10^{11}\) N m–2 ), both having a radius \(1.4\) mm, are connected end to end. When a load is applied, the net stretch of the combined wires is found to be \(1.4\) mm. The magnitude of the load applied, in Newtons, will be: \(\left (\text{use},~\pi=\dfrac{22}{7} \right ) \)
1. \(360\)
2. \(180\)
3. \(1080\)
4. \(154\)
1. \(360\)
2. \(180\)
3. \(1080\)
4. \(154\)
Subtopic: Young's modulus |
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In an experiment to determine Young's modulus, steel wires of five different lengths ( \(1,2,3,4\) and \(5~\text m\) ) but of the same cross-section (\(2~\text{mm}^2\)) were taken and curves between extension and load were obtained. The slope (extension/load) of the curves was plotted with the wire length and the following graph is obtained. If Young's modulus of a given steel wire is \(x\times 10^{11}~\text{N/m}^2,\) then the value of \(x\) is:
1. \(1\)
2. \(2\)
3. \(3\)
4. \(4\)
1. \(1\)
2. \(2\)
3. \(3\)
4. \(4\)
Subtopic: Stress - Strain Curve |
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The force required to stretch a wire of cross-section \(1\) cm2 to double its length will be:
(Given Young’s modulus of the wire \(=2\times10^{11}\) N/m2)
1. \(1\times10^{7}\) N
2. \(1.5\times10^{7}\) N
3. \(2\times10^{7}\) N
4. \(2.5\times10^{7}\) N
(Given Young’s modulus of the wire \(=2\times10^{11}\) N/m2)
1. \(1\times10^{7}\) N
2. \(1.5\times10^{7}\) N
3. \(2\times10^{7}\) N
4. \(2.5\times10^{7}\) N
Subtopic: Young's modulus |
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A wire of natural length \(L\) is suspended vertically from a fixed point. The length changes to \(L_1\) and \(L_2\) when masses \(1\) kg and \(2\) kg are suspended, respectively, from its free end. The value of \(L\) is:
| 1. | \(\sqrt{L_1L_2} \) | 2. | \(\dfrac{L_1+L_2}{2}\) |
| 3. | \(2L_1-L_2 \) | 4. | \(3L_1-2L_2\) |
Subtopic: Young's modulus |
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If the length of a wire is doubled and its radius is halved compared to their respective initial values, then, Young’s modulus of the material of the wire will:
| 1. | remain the same. |
| 2. | become \(8\) times its initial value. |
| 3. | become \({1 \over 4}\)th of its initial value. |
| 4. | become \(4\) times its initial value. |
Subtopic: Young's modulus |
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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
Subtopic: Stress - Strain |
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The bulk modulus of a liquid is \(3\times10^{10}\) Nm–2. The pressure required to reduce the volume of liquid by \(2\text{%}\) is:
1. \(3\times10^{8}\) Nm–2
2. \(9\times10^{8}\) Nm–2
3. \(6\times10^{8}\) Nm–2
4. \(12\times10^{8}\) Nm–2
1. \(3\times10^{8}\) Nm–2
2. \(9\times10^{8}\) Nm–2
3. \(6\times10^{8}\) Nm–2
4. \(12\times10^{8}\) Nm–2
Subtopic: Shear and bulk modulus |
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Level 1: 80%+
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