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Q. No.A sphere of small size is at the bottom of a lake of depth \(200 ~\text m.\) Due to pressure its fractional change in volume is \(\alpha\times 10^{-7}.\) What is the value of \(\alpha,\) if the bulk modulus of the sphere is \(5 × 10^{12}~\text{Pa}?\) (Use \(g = 10 ~\text{m/s}^2\) )
1. \(5\)
2. \(4\)
3. \(6\)
4. \(10\)
Subtopic: Shear and bulk modulus |
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If the area of the cross-section is halved and the length of the wire having Young’s modulus \(Y\) is doubled, then its Young’s modulus will become:
1. \(Y\)
2. \(4Y\)
3. \(\frac{Y}{2}\)
4. \( \frac{Y}{4}\)
1. \(Y\)
2. \(4Y\)
3. \(\frac{Y}{2}\)
4. \( \frac{Y}{4}\)
Subtopic: Young's modulus |
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A uniform wire of length \(L\) and radius \( r\) is subjected to a stretching force \(F,\) resulting in an elongation of \( \Delta L.\) If both the force \(F\) and the radius \(r\) are reduced to half their original values, what will be the new elongation of the wire?
| 1. | \( \dfrac{\Delta L}{2}\) | 2. | \( \Delta L\) |
| 3. | \( 4\Delta L\) | 4. | \(2\Delta L\) |
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. \(\left(\frac{y}{x}\right)^2 \frac{n}{m} \)
2. \(\left(\frac{x}{y}\right)^2 \frac{n}{m} \)
3. \(\left(\frac{x}{y}\right)^2 \frac{m}{n}\)
4. \(\left(\frac{y}{x}\right)^2\frac{m}{n}\)
1. \(\left(\frac{y}{x}\right)^2 \frac{n}{m} \)
2. \(\left(\frac{x}{y}\right)^2 \frac{n}{m} \)
3. \(\left(\frac{x}{y}\right)^2 \frac{m}{n}\)
4. \(\left(\frac{y}{x}\right)^2\frac{m}{n}\)
Subtopic: Young's modulus |
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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. \(9~\text{rad s}^{-1}\)
(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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Wire \({A}\) and \({B}\) have their Young's modulii in the ratio \(1:3\) area of the cross-section in the ratio of \(1:2\) and lengths in the ratio of \(3:4.\) If the same force is applied on the two wires to elongate then the ratio of elongation is equal to:
1. \(8:1\)
2. \(1:12\)
3. \(1:8\)
4. \(9:2\)
1. \(8:1\)
2. \(1:12\)
3. \(1:8\)
4. \(9:2\)
Subtopic: Young's modulus |
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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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Two blocks, one with a mass of \(2~\text{kg}\) and the other with a mass of \(1.14~\text{kg},\) are suspended by steel and brass wires, respectively, as shown in the figure. Given Young's moduli for steel and brass as \(2\times10^{11}~\text{N}/\text{m}^2\) and \(1\times10^{11}~\text{N}/\text{m}^2\) respectively, what is the change in the length for the steel wire?
| 1. | \(3.2 ~\mu \text{m}\) | 2. | \(1.6 ~\mu \text{m}\) |
| 3. | \(0.8 ~\mu \text{m}\) | 4. | \(4.8 ~\mu \text{m}\) |
Subtopic: Elasticity |
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Choose the correct expression that relates Poisson’s ratio \(\sigma,\) bulk modulus \(B,\) and modulus of rigidity \(G.\)
1. \(\mathit{\sigma}{=}\dfrac{{3}{B}{-}{2}{G}}{{2}{G}{+}{6}{B}}\)
2. \(\mathit{\sigma}{=}\dfrac{{6}{B}{+}{2}{G}}{{3}{B}{-}{2}{G}}\)
3. \(\mathit{\sigma}{=}\dfrac{9BG}{{3}{B}{+}{G}}\)
4. \({B}{=}\dfrac{{3}\mathit{\sigma}{-}{3}{G}}{{6}\mathit{\sigma}{+}{2}{G}}\)
1. \(\mathit{\sigma}{=}\dfrac{{3}{B}{-}{2}{G}}{{2}{G}{+}{6}{B}}\)
2. \(\mathit{\sigma}{=}\dfrac{{6}{B}{+}{2}{G}}{{3}{B}{-}{2}{G}}\)
3. \(\mathit{\sigma}{=}\dfrac{9BG}{{3}{B}{+}{G}}\)
4. \({B}{=}\dfrac{{3}\mathit{\sigma}{-}{3}{G}}{{6}\mathit{\sigma}{+}{2}{G}}\)
Subtopic: Elasticity |
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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
Subtopic: Stress - Strain |
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