Practice Questions

Q8. Two moles of an ideal gas, with CV CP = 35 , are mixed with three moles of another ideal gas CVCP = 34 . The value of CP for the mixture is CV (1) 1.45 (2) 1.50 (3) 1.47 (4) 1.42

Q8. Consider two ideal diatomic gases A and B at some temperature T . Molecules of the gas A are rigid, and have a mass m . Molecules of the gas B have an additional vibrational mode and have a mass m . The ratio of the 4 specific heats (C V )Aand ( CV )B of gas A and B, respectively is: JEE Main 2020 (09 Jan Shift 1) JEE Main Previous Year Paper (1) 7 : 9 (2) 5 : 9 (3) 3 : 5 (4) 5 : 7

Q8. A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as shown in the figure. The radius of vessel is 5 cm and the angular speed of rotation is ω rad s−1 . The difference in the height, h (in cm) of liquid at the Centre of vessel and at the sides of the vessel will be : JEE Main 2020 (02 Sep Shift 1) JEE Main Previous Year Paper (1) 2ω2 (2) 5ω2 25g 2g (3) 25ω2 (4) 2ω2 2g 5g

Q8. A Carnot engine having an efficiency of 1 is being used as a refrigerator. If the work done on the refrigerator 10 is 10 J, the amount of heat absorbed from the reservoir at a lower temperature is (1) 99 J (2) 100 J (3) 1 J (4) 90 J JEE Main 2020 (08 Jan Shift 2) JEE Main Previous Year Paper

Q8. A thermodynamic cycle xyzx is shown on a V - T diagram. The P - V diagram that best describes this cycle is: (Diagrams are schematic and not to scale) JEE Main 2020 (08 Jan Shift 1) JEE Main Previous Year Paper (1) (2) (3) (4)

Q8. Two ideal Carnot engines operate in cascade (all heat given up by one engine is used by the other engine to produce work) between temperatures, T1 and T2 . The temperature of the hot reservoir of the first engine is T1 and the temperature of the cold reservoir of the second engine is T2 . T is temperature of the sink of first engine which is also the source for the second engine. How is T related to T1 and T2 , if both the engines perform equal amount of work? JEE Main 2020 (07 Jan Shift 2) JEE Main Previous Year Paper (1) T = 2T1T2 (2) T = T1+T22 T1+T2 (3) T = √T1T2 (4) T = 0

Q8. A ring is hung on a nail. It can oscillate, without slipping or sliding (i) in its plane with a time period T1 and (ii) back and forth in a direction perpendicular to its plane, with a period T2. The ratio T1 will be : T2 (1) 2 (2) 2 √3 3 (3) 3 (4) √2 √2 3

Q8. A calorimeter of water equivalent 20 g contains 180 g of water at 25°C. ′m′' grams of steam at 100°C is mixed in it till the temperature of the mixture is 31°C. The value of ′m′ is close to (Latent heat of water = 540 cal g−1 , specific heat of water = 1 cal g−1°C−1 ) (1) 2 (2) 4 (3) 3. 2 (4) 2. 6

Q8. Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is 1 : 4, the ratio of their diameters is: (1) √2 : 1 (2) 1 : 2 (3) 2 : 1 (4) 1 : √2

Q8. Two isolated conducting spheres S1 and S2 of radius 32 R and 31 R have 12 μC and −3 μC charges, respectively, and are at a large distance from each other, They are now connected by a conducting wire. A long time after this is done the charges on S1 and S2 are respectively: (1) 4. 5 μC of both (2) +4. 5 μC and −4. 5 μC (3) 3 μC and 6 μC (4) 6 μC and 3 μC

Q8. Number of molecules in a volume of 4 cm3 of a perfect monoatomic gas at some temperature T and at a pressure of 2 cm of mercury is close to? (Given, mean kinetic energy of a molecule (at T) is 4 × 10−14 erg, g = 980 cm s−2 density of mercury = 13. 6 g cm−3 ) (1) 4 .8 ×1018 (2) 4. 0 × 1016 (3) 5. 8 × 1016 (4) 5. 8 × 1018

Q8. A cube of metal is subjected to a hydrostatic pressure 4 GPa . The percentage change in the length of the side of the cube is close to : (Given bulk modulus of metal, B = 8 × 1010 Pa ) (1) 5 (2) 0. 6 (3) 20 (4) 1. 67

Q8. The displacement time graph of a particle executing SHM is given in figure: (sketch is schematic and not to scale) Which of the following statements is/are true for this motion? (A) The force is zero at t = 3T4 (B) The magnitude of acceleration is maximum at t = T (C) The speed is maximum at t = T4 (D) The P. E. is equal to K. E. of the oscillation at t = T2 (1) (A), (B) and (C) (2) (B), (C) and (D) (3) (A), (B) and (D) (4) (A) and (D)

Q8. Match the Cp ratio for ideal gases with different type of molecules: Cv Molecule Type Cp/Cv (A) Monoatomic (I) 7/5 (B) Diatomic rigid molecules (II) 9/7 (C) Diatomic non-rigid molecules (III) 4/3 (D) Triatomic rigid molecules (IV) 5/3 (1) (A) – (IV), (B) – (II), (C) – (I), (D) – (III) (2) (A) – (III), (B) – (IV), (C) – (II), (D) – (I) (3) (A) – (IV), (B) – (I), (C) – (II), (D) – (III) (4) (A) – (II), (B) – (III), (C) – (I), (D) – (IV)

Q8. In a dilute gas at pressure P and temperature ' t', the time between successive collision of a molecule varies with T as : (1) T (2) 1 √T (3) 1 (4) √T T

Q8. An object of mass m is suspended at the end of a massless wire of length L and area of cross-section, A. Young modulus of the material of the wire is Y . If the mass is pulled down slightly its frequency of oscillation along the vertical direction is : (1) 1 (2) 1 A f = 2π √mLY A f = 2π √YmL (3) 1 (4) 1 L f = 2π √mAV L f = 2π √YmA

Q9. A stationary observer receives sound from two identical tuning forks, one of which approaches and the other one recedes with the same speed (much less than the speed of sound). The observer hears 2 beats/sec . The oscillation frequency of each tuning fork is v0 = 1400 Hz and the velocity of sound in air is 350 m/s . The speed of each tuning fork is close to: (1) 1 m/s (2) 1m/s 2 (3) 4 1 m/s (4) 81 m/s →

Q9. For a transvers wave travelling, along a straight line, the distance between two peaks (crests) is 5 m , while the distance between one crest and one trough is 1. 5 m. The possible wavelengths (in m ) of the waves are: (1) 1, 3, 5 (2) 11 , 13 , 51 , . . . . . (3) 1, 2, 3, . . . . (4) 12 , 14 , 61 , . . . . .

Q9. Consider a mixture of n moles of helium gas and 2n moles of oxygen gas (molecules taken to be rigid) as an ideal gas. Its CP value will be: CV (1) 19 (2) 67 13 45 (3) 40 (4) 23 27 15

Q9. Three harmonic waves having equal frequency v and same intensity I0 , have phase angles 0, π4 and −π4 respectively. When they are superimposed the intensity of the resultant wave is close to: (1) 5.8I0 (2) 0.2I0 (3) 3I0 (4) I0

Q9. A sound source S is moving along a straight track with speed v , and is emitting sound of frequency v0 .An observer is standing at a finite distance, at the point O, from the track. The time variation of frequency heard by observer is best represented by : (to represents the instant when the distance between the source and observer is minimum) (1) (2) (3) (4) JEE Main 2020 (06 Sep Shift 1) JEE Main Previous Year Paper

Q9. Assuming the nitrogen molecule is moving with r. m. s. velocity at 400 K, the de-Broglie wave length of nitrogen molecule is close to : (Given : nitrogen molecule weight : 4 .64 ×10−26 kg, Boltzman constant : 1 .38 ×10−23 J K−1 , Planck constant : 6 .63 ×10−34 J s) ∘ ∘ (1) (2) 0. 24 A 0. 20 A ∘ ∘ (3) (4) 0. 34 A 0. 44 A

Q9. To raise the temperature of a certain mass of gas by 50 °C at a constant pressure, 160 calories of heat is required. When the same mass of gas is cooled by 100°C at constant volume, 240 calories of heat is released. How many degrees of freedom does each molecule of this gas have (assume gas to be ideal)? (1) 5 (2) 6 (3) 3 (4) 7

Q9. A bullet of mass 5 gram, travelling with a speed of 210 m s−1 strikes a fixed wooden target. One half of its kinetic energy is converted into heat in the wood. The rise of temperature of the bullet if the specific heat of its material is 0. 030 (gram °C)−1 (1 calorie = 4 .2 ×107 ergs) close to : (1) 87. 5°C (2) 83. 3°C (3) 119. 2°C (4) 38. 4°C

Q9. The plot that depicts the behavior of the mean free time τ (time between two successive collisions) for the molecules of an ideal gas, as a function of temperature (T), qualitatively, is: (Graphs are schematic and not drawn to scale) (1) (2) (3) (4)