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Q. No.A wire is suspended from the ceiling and stretched under the action of a weight \(F\) suspended from its other end. The force exerted by the ceiling on it is equal and opposite to the weight.
(a)
Tensile stress at any cross-section \(A\) of the wire is \(F/A.\)
(b)
Tensile stress at any cross-section is zero.
(c)
Tensile stress at any cross-section \(A\) of the wire is \(2F/A.\)
(d)
Tension at any cross-section \(A\) of the wire is \(F.\)
The correct statements are:
1.
(a), (b)
2.
(a), (d)
3.
(b), (c)
4.
(a), (c)
The correct statements are:
Subtopic: Stress - Strain |
80%
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A rod of length \(l\) and negligible mass is suspended at its two ends by two wires of steel (wire \(A\)) and aluminium (wire \(B\)) of equal lengths (figure). The cross-sectional areas of wires \(A\) and \(B\) are \(1.0~\text{mm}^2\) and \(2.0~\text{mm}^2\) respectively.
\((Y_{\text{Al}}=70\times10^9~\text{N/m}^2\) and \(Y_{\text{steel}}=200\times10^9~\text{N/m}^2)\)
The correct statements are:
1. (b), (c)
2. (a), (d)
3. (b), (d)
4. (c), (d)
\((Y_{\text{Al}}=70\times10^9~\text{N/m}^2\) and \(Y_{\text{steel}}=200\times10^9~\text{N/m}^2)\)
| (a) | Mass \(m\) should be suspended close to wire \(A\) to have equal stresses in both wires. |
| (b) | Mass \(m\) should be suspended close to \(B\) to have equal stresses in both wires. |
| (c) | Mass \(m\) should be suspended in the middle of the wires to have equal stresses in both wires. |
| (d) | Mass \(m\) should be suspended close to wire \(A\) to have equal strain in both wires. |
The correct statements are:
1. (b), (c)
2. (a), (d)
3. (b), (d)
4. (c), (d)
Subtopic: Elasticity | Stress - Strain |
From NCERT
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For an ideal liquid:
Choose the correct option from the options given below:
| (a) | The bulk modulus is infinite. |
| (b) | The bulk modulus is zero. |
| (c) | The shear modulus is infinite. |
| (d) | The shear modulus is zero. |
Choose the correct option from the options given below:
| 1. | (a) and (d) only |
| 2. | (b) and (d) only |
| 3. | (b) and (c) only |
| 4. | (c) and (d) only |
Subtopic: Shear and bulk modulus |
65%
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A copper and a steel wire of the same diameter are connected end to end. A deforming force \(F\) is applied to this composite wire which causes a total elongation of \(1\) cm. The two wires will have:
Choose the correct option:
| (a) | the same stress | (b) | different stress |
| (c) | the same strain | (d) | different strain |
Choose the correct option:
| 1. | (a), (b) | 2. | (a), (d) |
| 3. | (b), (c) | 4. | (c), (d) |
Subtopic: Young's modulus |
79%
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The stress-strain graphs for the two materials are shown in the figure. (assumed same scale)
| (a) | Material (ii) is more elastic than material (i) and hence material (ii) is more brittle |
| (b) | Material (i) and (ii) have the same elasticity and the same brittleness |
| (c) | Material (ii) is elastic over a larger region of strain as compared to (i) |
| (d) | Material (ii) is more brittle than material (i) |
The correct statements are:
1. (a), (c)
2. (c), (d)
3. (b), (c)
4. (b), (d)
Subtopic: Stress - Strain Curve |
72%
From NCERT
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Consider two cylindrical rods of identical dimensions, one of rubber and the other of steel. Both the rods are fixed rigidly at one end of the roof. A mass \(M\) is attached to each of the free ends at the centre of the rods.
| 1. | Both the rods will elongate but there shall be no perceptible change in shape. |
| 2. | The steel rod will elongate and change shape but the rubber rod will only elongate. |
| 3. | The steel rod will elongate without any perceptible change in shape but the rubber rod will elongate and the shape of the bottom edge will change to an ellipse. |
| 4. | The steel rod will elongate without any perceptible change in shape but the rubber rod will elongate with the shape of the bottom edge tapered to a tip at the centre. |
Subtopic: Elasticity |
58%
From NCERT
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A rectangular frame is to be suspended symmetrically by two strings of equal length on two supports (figure). It can be done in one of the following three ways;
The tension in the strings will be:
| 1. | the same in all cases. | 2. | least in (a). |
| 3. | least in (b). | 4. | least in (c). |
Subtopic: Stress - Strain |
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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. | \(\dfrac{x^2}{2L}\) |
Subtopic: Stress - Strain |
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A rigid bar of mass \(M\) is supported symmetrically by three wires each of length \(l\). Those at each end are of copper and the middle one is of iron. The ratio of their diameters, if each is to have the same tension, is equal to:
| 1. | \(\dfrac{Y_{\text{copper}}}{ Y_{\text{iron}}}\) | 2. | \({\sqrt{\dfrac{Y_{\text{iron}}}{Y_{\text{copper}}}}}\) |
| 3. | \({\dfrac{Y^{2}_{\text{iron}}}{Y^{2}_{\text{copper}}}}\) | 4. | \({\dfrac{Y_{\text{iron}}}{Y_{\text{copper}}}}\) |
Subtopic: Young's modulus |
82%
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A spring is stretched by applying a load to its free end. The strain produced in the spring is:
1. volumetric2. shear
3. longitudinal and shear
4. longitudinal
Subtopic: Stress - Strain |
62%
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