Assertion (A): Water is considered unsuitable for use in thermometers.
Reason (R): Thermal Expansion of water is non-uniform.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
Assertion (A) is true. Water exhibits anomalous expansion between \(0^{\circ}\text{C}\) and \(4^{\circ}\text{C}\), making it unreliable for linear temperature scales. Reason (R) is true.
The non-uniform thermal expansion of water (especially its contraction then expansion) is why it's unsuitable for thermometers. (R) is the correct explanation for (A).
Assertion (A): The temperature of a metallic rod is raised by a temperature \(\Delta t\) so that its length becomes double. The value of \(\alpha\) (coefficient of linear expansion) is given by \(\frac{\log_e (2)}{\Delta t}\).
Reason (R): Coefficient of linear expansion is defined as \(\frac{1}{l} \frac{dl}{dt}\).
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
Reason (R) is the correct definition for the instantaneous coefficient of linear expansion (assuming \(t\) is temperature), so it is true. Integrating \(dl/l = \alpha dT\) with constant \(\alpha\) gives \(ln(l/l_0) = \alpha \Delta T\), so \(l = l_0 e^{\alpha \Delta T}\). If \(l = 2l_0\), then \(2 = e^{\alpha \Delta T}\), leading to \(\alpha = \frac{ln 2}{\Delta T}\).
So Assertion (A) is true. (R) provides the foundational definition from which (A) is derived, thus it's the correct explanation.
Assertion (A): Liquids usually expand more than solids.
Reason (R): The intermolecular forces in liquids are weaker than in solids.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
Assertion (A) is true as liquids typically have higher coefficients of thermal expansion than solids. Reason (R) is true because weaker intermolecular forces in liquids allow molecules to move more freely and separate further upon heating.
(R) correctly explains (A), as the weaker forces enable greater thermal expansion.
Assertion (A): Temperature of a rod is increased and again cooled to same initial temperature then its final length is equal to original length.
Reason (R): For a small temperature change, length of a rod varies as \( l = l_0 (1+\alpha \Delta T) \) provided \( \alpha \Delta T is small \). Here symbol have their usual meaning.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Assertion is true as thermal expansion is reversible for elastic materials. Reason is the formula for linear expansion, \( l = l_0 (1+\alpha \Delta T) \), which confirms the assertion if \( \Delta T \) is reversed. Thus, both are true and (R) explains (A).
Assertion (A): A temperature change which increases the length of a steel rod by ( 1% ) will increase its volume by ( 3% ).
Reason (R): The coefficient of volume expansion is nearly three times the coefficient of linear expansion.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Assertion (A) is true. If \( \frac{\Delta L}{L_0} = \alpha \Delta T = 0.01 \), then \( \frac{\Delta V}{V_0} = \gamma \Delta T \). Reason (R) is true, stating \( \gamma \approx 3\alpha \). Substituting, \( \frac{\Delta V}{V_0} \approx 3 (\alpha \Delta T) = 3(0.01) = 0.03 \), or ( 3% ). Thus, both are true and (R) correctly explains (A).
Assertion (A): When hot water is suddenly poured in cold beaker of thick glass, the beaker cracks.
Reason (R): Glass is bad conductor of heat and outer surface of the beaker does not expand.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
Thick glass is a poor thermal conductor. When hot water is poured, the inner surface expands rapidly due to heating, while the outer surface remains cold and resists expansion.
This differential thermal expansion creates significant stress, causing the glass to crack. Both A and R are true, and R is the correct explanation for A.
Assertion (A): The expanded length l of a rod of original length l_0 is not correctly given by assuming \(\alpha\) to be constant with T \( \l = \l_0 (1 + \alpha \Delta T)\), if \(\alpha \Delta T\) is large.
Reason (R): It is given by \(l = \l_0 \text{e}^{\alpha \Delta T}\), which cannot be treated as being approximately equal to \(l_0 (1 + \alpha \Delta T)\text{ for large value of }\alpha \Delta T\).
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
The standard linear expansion formula \(ell = \ell_0 (1 + \alpha \Delta T)\text{ is an approximation valid for small }\alpha \Delta T\), derived from the exponential form \(ell = \ell_0 \text{e}^{\alpha \Delta T}\). If \(alpha \Delta T\) is large, this approximation fails. Both (A) and (R) are true, and (R) correctly explains (A).