Consider the following statements.
Statement A: Velocity of sound in gaseous medium depends on molar mass of gas.
Statement B: Mechanical wave require a material medium for their propagation.
Statement C: Speed of sound is less in humid air.
Which of the statement(s) is/are correct?
1. Only statements A and B
2. Only statements B and C
3. Only statements A and C
4. All statements A, B and C
View Answer
Velocity of sound is given by \(v = \sqrt{\frac{\gamma RT}{M}}\), so it depends on molar mass \(M\). Mechanical waves require a material medium. Humid air has lower density than dry air, which increases the speed of sound, making Statement C incorrect.
Assertion (A): As the temperature of the blackbody increases, the wavelength at which the spectral intensity \(E_\lambda\) is maximum decreases.
Reason (R): The wavelength at which the spectral intensity will be maximum for a black body is proportional to the fourth power of its absolute temperature.
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 according to Wien's displacement law, \(\lambda_{max} T = \text{constant}\). Reason (R) is false as \(\lambda_{max}\) is inversely proportional to temperature, not proportional to \(T^4\). \(E = \sigma T^4\) relates total emissive power to temperature.
Assertion (A): Two metallic spheres of same size, one of copper and the other of aluminium, heated to the same temperature, will cool at the same rate when they are suspended in the same enclosure.
Reason (R): The rate of cooling of a body depends only on the excess of temperature of the body over the surroundings.
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 false because cooling rate depends on material properties like specific heat capacity and emissivity, which differ for copper and aluminium. Reason (R) is false.
Newton's Law of Cooling shows rate depends on surface area and emissivity, not just temperature difference.
Assertion (A): Colour of a glowing black body changes on increasing its temperature.
Reason (R): Spectral emissive power associated with each wavelength does not increase in same proportion on increasing temperature of the Black Body.
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 due to Wien's displacement law; \(\lambda_{max}\) shifts to shorter wavelengths with increasing temperature. Reason (R) is true. Planck's law shows spectral emissive power increases disproportionately for different wavelengths with temperature. (R) explains (A) as this disproportionate increase causes the color shift.
Assertion (A): Specific heat capacity of a substance in \(\text{cal/g}^{\circ}\text{C}\) is greater than its specific heat capacity in \(\text{cal/g}^{\circ}\text{F}\).
Reason (R): Magnitude (temperature difference) of \(1^{\circ}\text{C}\) is greater than the magnitude of \(1^{\circ}\text{F}\).
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 true because a \(1^{\circ}\text{C}\) temperature change is equivalent to a \(1.8^{\circ}\text{F}\) change. Assertion (A) is true. Since \(c = \frac{Q}{m \Delta T}\) and \(1^{\circ}\text{C} = 1.8^{\circ}\text{F}\), \(c_{\text{cal/g}^{\circ}text{C}}\) will be \(1.8 \times c_{\text{cal/g}^{\circ}\text{F}}\) for the same substance. Therefore, (R) is the correct explanation of (A).
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).