Q. No.A steel wire with a cross-sectional area of \(3\times 10^{-6} \) m2 can withstand a maximum strain of \(10^{-3}.\) Young's modulus of steel is \(Y=2\times 10^{11} \) N/m2. The maximum mass that the wire can hold is:
( take \(g=10\) m/s2)
1. \(50\) kg
2. \(60\) kg
3. \(70\) kg
4. \(80\) kg
( take \(g=10\) m/s2)
1. \(50\) kg
2. \(60\) kg
3. \(70\) kg
4. \(80\) kg
Subtopic: Young's modulus |
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A wire of length \(L\) and radius \(r \) is clamped rigidly at one end. When the other end of the wire is pulled by a force \(F,\) its length increases by \(5~\text{cm}. \) Another wire of the same material of length \(4L\) and radius \(4r \) is pulled by a force \(4F \) under the same conditions. The increase in length of this wire is:
1. \(3~\text{cm}\)
2. \(5~\text{cm}\)
3. \(10~\text{cm}\)
4. \(6~\text{cm}\)
1. \(3~\text{cm}\)
2. \(5~\text{cm}\)
3. \(10~\text{cm}\)
4. \(6~\text{cm}\)
Subtopic: Young's modulus |
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The dimensions of stress, strain, and Young's modulus of elasticity are, respectively:
| 1. | \(\left[MT^{-2}\right], ~[L]~,~\left[ML^{-1}T^{-2}\right]\) |
| 2. | \(\left[ML^{-1}T^{-2}\right],~\left[M^0L^{0}T^{0}\right],~\left[ML^{-1}T^{-2}\right]\) |
| 3. | \(\left[M^0L^0T^0\right],~[L]~,~\left[ML^{-1}T^{-2}\right]\) |
| 4. | \(\left[MLT^{-2}\right]~,\left[ML^2T^{-2}\right],~\left[MT^{-2}\right]\) |
Subtopic: Young's modulus |
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The elongation of a wire on the surface of the Earth is \(10^{-4}\text{ m}.\) The same wire, of the same dimensions, elongates by \( 6 \times 10^{-5} \text{ m}\) on another planet. The acceleration due to gravity on the planet will be:
(take acceleration due to gravity on the surface of the Earth as \(10\text{ m/s}^2\))
1. \(5\text{ m/s}^2\)
2. \(6\text{ m/s}^2\)
3. \(7\text{ m/s}^2\)
4. \(8\text{ m/s}^2\)
(take acceleration due to gravity on the surface of the Earth as \(10\text{ m/s}^2\))
1. \(5\text{ m/s}^2\)
2. \(6\text{ m/s}^2\)
3. \(7\text{ m/s}^2\)
4. \(8\text{ m/s}^2\)
Subtopic: Young's modulus |
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A steel wire has a proportional limit of \(8 \times 10^8~\text{N/m}^2\) and a Young’s modulus of \(2 \times 10^{11}~\text{N/m}^2.\) If the wire is \(1~\text{m}\) long, what is the maximum elongation it can undergo without exceeding the proportional limit?
| 1. | \(2~\text{mm}\) | 2. | \(4~\text{mm}\) |
| 3. | \(1~\text{mm}\) | 4. | \(8~\text{mm}\) |
Subtopic: Stress - Strain Curve | Young's modulus |
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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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The equivalent of spring constant \(k\) for a wire of length \(L\), cross-sectional area, and Young's modulus \(Y\)is:
1. \(\dfrac{Y L}{A} \)
2. \(\dfrac{YA}{L}\)
3. \(\dfrac{A L}{Y}\)
4. \( YAL \)
1. \(\dfrac{Y L}{A} \)
2. \(\dfrac{YA}{L}\)
3. \(\dfrac{A L}{Y}\)
4. \( YAL \)
Subtopic: Young's modulus |
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A vertical wire \(5~\text m\) long and \(8\times 10^{-3}~\text{cm}^2\) cross-sectional area has Young's modulus \(=200~\text {GPa}\) (as shown in the figure). What will be the extension in its length, when a \(2~\text{kg}\) object is fastened to its free end?
1. \(0.625~\text{mm}\)
2. \(0.65~\text{mm}\)
3. \(0.672~\text{mm}\)
4. \(0.72~\text{mm}\)
1. \(0.625~\text{mm}\)
2. \(0.65~\text{mm}\)
3. \(0.672~\text{mm}\)
4. \(0.72~\text{mm}\)
Subtopic: Young's modulus |
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The radii and Young's moduli of two uniform wires \(A\) and \(B\) are in the ratio \(2:1\) and \(1:2\) respectively. Both wires are subjected to the same longitudinal force. If the increase in length of the wire \(A\) is \(1\%\), the increase in the length of the wire \(B\) will be:
| 1. | \(1.5\%\) | 2. | \(2.0\%\) |
| 3. | \(2.5\%\) | 4. | \(3.0\%\) |
Subtopic: Young's modulus |
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Two forces \( F_1\) and \( F_2\) are applied on two rods \( P\) and \(Q\) of the same materials such that elongation in rods are same. If the ratio of their radii is \( x : y \) and the ratio of length is \(m:n,\) then the ratio of forces \( F_1:F_2\) is:
1. \(\left(\dfrac{y}{x}\right)^2 \dfrac{n}{m} \)
2. \(\left(\dfrac{x}{y}\right)^2 \dfrac{n}{m} \)
3. \(\left(\dfrac{x}{y}\right)^2 \dfrac{m}{n}\)
4. \(\left(\dfrac{y}{x}\right)^2\dfrac{m}{n}\)
1. \(\left(\dfrac{y}{x}\right)^2 \dfrac{n}{m} \)
2. \(\left(\dfrac{x}{y}\right)^2 \dfrac{n}{m} \)
3. \(\left(\dfrac{x}{y}\right)^2 \dfrac{m}{n}\)
4. \(\left(\dfrac{y}{x}\right)^2\dfrac{m}{n}\)
Subtopic: Young's modulus |
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