Q. No.A rod \(\mathrm{A}\) has a coefficient of thermal expansion \((\alpha_A)\) which is twice of that of rod \(\mathrm{B}\) \((\alpha_B)\). The two rods have length \(l_A,~l_B\) where \(l_A=2l_B\). If the two rods were joined end-to-end, the average coefficient of thermal expansion is:
| 1. | \(\alpha_A\) | 2. | \(\dfrac{2\alpha_A}{6}\) |
| 3. | \(\dfrac{4\alpha_A}{6}\) | 4. | \(\dfrac{5\alpha_A}{6}\) |
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| 1. | \(5 \alpha \) | 2. | \(\dfrac{3 \alpha}{5} \) |
| 3. | \(\dfrac{5 \alpha}{3} \) | 4. | \(15 \alpha\) |
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| 1. | \(\left(\dfrac{\Delta I_0}{I_0}\right)\dfrac{1}{\Delta\theta}\) |
| 2. | \(\dfrac12\left(\dfrac{\Delta I_0}{I_0}\right)\dfrac{1}{\Delta\theta}\) |
| 3. | \(\dfrac15\left(\dfrac{\Delta I_0}{I_0}\right)\dfrac{1}{\Delta\theta}\) |
| 4. | \(2\left(\dfrac{\Delta I_0}{I_0}\right)\dfrac{1}{\Delta\theta}\) |
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| 1. | \({\Large\gamma}_L\theta\times{\large p}_0 ~\) |
| 2. | \({\Large\frac{\theta}{273}}{\large p}_0\) |
| 3. | \({\dfrac{{\Large\gamma}_L\theta}{273}}{\large p}_0\) |
| 4. | \(\Big({\Large\gamma}_L\theta+{\Large\frac{\theta}{273}}\Big){\large p}_0 \) |
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| 1. | is \(2\alpha\) |
| 2. | is \(4\alpha\) |
| 3. | can be any value between \(\alpha\) and \(3\alpha\) |
| 4. | can be any value between \(2\alpha\) and \(3\alpha\) |
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| 1. | \(l+\Delta l\) | 2. | \(l+\dfrac{\Delta l}{2}\) |
| 3. | \(l+\dfrac{\Delta l}{4}\) | 4. | \(l+\dfrac{3\Delta l}{4}\) |
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| 1. | \((^\circ\text C)^ {-1}\) | 2. | \(\text{m}^3/^\circ\text C\) |
| 3. | \(^\circ\text C\) | 4. | \(^\circ\text C/\text{m}^3\) |
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| 1. | \(L(1+\gamma\theta)\) | 2. | \(L\left(1+\dfrac\gamma2\theta\right)\) |
| 3. | \(L\left(1+\dfrac\gamma3\theta\right)\) | 4. | \(L\left(1+\dfrac{2\gamma}3\theta\right)\) |
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1. \(1:1\)
2. \(2:1\)
3. \(1:2\)
4. \(3:1\)
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| 1. | move slightly upward, but remain submerged |
| 2. | move slightly down, but remain submerged |
| 3. | rise up to the surface |
| 4. | sink within the liquid |
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