Practice Questions

Q10.A heat source at T = 103 K is connected to another heat reservoir at T = 102 K by a copper slab which is 1 m thick. Given that the thermal conductivity of copper is 0 .1 W K−1 m−1 , the energy flux through it in the steady-state is: (1) 65 W m−2 (2) 120 W m−2 (3) 90 W m−2 (4) 200 W m−2

Q10.A rod, of length 𝐿 at room temperature and uniform area of cross section 𝐴, is made of a metal having coefficient of linear expansion 𝛼 / °𝐶 It is observed that an external compressive force 𝐹 is applied on each of its ends, prevents any change in the length of the rod when its temperature rises by ∆𝑇 K Young's modulus, 𝑌 for this metal is: 𝐹 2𝐹 (1) (2) 𝐴𝛼∆𝑇- 273 𝐴𝛼∆𝑇 𝐹 𝐹 (3) (4) 𝐴𝛼∆𝑇 2𝐴 𝛼∆𝑇 JEE Main 2019 (09 Jan Shift 1) JEE Main Previous Year Paper

Q10.A sample of an ideal gas is taken through the cyclic process abca as shown in the figure. The change in the internal energy of the gas along the path ca is -180 J . The gas absorbs 250 J of heat along the path ab and 60 J along the path bc . The work done by the gas along the path abc is: (1) 130 J (2) 100 J (3) 120 J (4) 140 J JEE Main 2019 (12 Apr Shift 1) JEE Main Previous Year Paper

Q10.A soap bubble, blown by a mechanical pump at the mouth of a tube increases in volume with time at a constant rate. The graph that correctly depicts the time dependence of pressure inside the bubble is given by: JEE Main 2019 (12 Jan Shift 2) JEE Main Previous Year Paper (1) (2) (3) (4)

Q11.The given diagram shows four processes i.e., isochoric, isobaric, isothermal and adiabatic. The correct assignment of the processes, in the same order is given by: (1) a d b c (2) d a b c (3) a d c b (4) d a c b

Q11.The specific heats, Cp and Cv of a gas of diatomic molecules, A, are given (in units of J mol−1 K−1 ) by 29 and 22, respectively. Another gas of diatomic molecules, B, has the corresponding values 30 and 21. If they are treated as ideal gases, then: (1) A has one vibrational mode and B has two (2) A has a vibrational mode but B has none. (3) Both A and B have a vibrational mode each. (4) A is rigid but B has a vibrational mode.

Q11.A particle is executing simple harmonic motion (SHM) of amplitude A, along the x -axis, about x = 0. When its potential Energy (PE) equal kinetic energy (KE), the position of the particle will be: (1) A (2) A 2 (3) A (4) A 2√2 √2

Q11.Two light identical springs of spring constant k are attached horizontally at the two ends of a uniform horizontal rod AB of length l and mass m. The rod is pivoted at its center 'O' and can rotate freely in horizontal plane. The other ends of the two springs are fixed to rigid supports as shown in figure. The rod is gently pushed through a small angle and released. The frequency of resulting oscillation is: (1) 1 (2) 1 2π √3km 2π √km (3) 1 (4) 1 2π √6km 2π √2km

Q11.An ideal gas is enclosed in a cylinder at pressure of 2 atm and temperature, 300 K. The mean time between two successive collisions is 6 × 10−8s. If the pressure is doubled and temperature is increased to 500 K, the mean time between two successive collisions will be close to: (1) 2 x 10−7s (2) 3 x 10−6s (3) 0. 5 x 10−8s (4) 4 x 10−8s

Q11.A thermally insulated vessel contains 150 g of water at 0°C . Then the air from the vessel is pumped out adiabatically. A fraction of water turns into ice and the rest evaporates at 0°C itself. The mass of evaporated water will be closest to: (Latent heat of vaporization of water = 2.10 × 106 J kg-1 and Latent heat of Fusion of water = 3.36 × 105 J kg-1 ) (1) 35 g (2) 20 g (3) 130 g (4) 150 g

Q11.For given gas at 1 atm pressure, rms speed of the molecules is 200 m/s at 127°C. At 2 atm pressure and at 227° C, the rms speed of the molecules will be: (1) 100 m/s (2) 80 m/s (3) 80√5 m/s (4) 100√5 m/s

Q11.The displacement of a damped harmonic oscillator is given by x(t) = e−0.1t cos(10πt + φ). Here t is in seconds. The time taken for its amplitude of vibration to drop to half of its initial value is close to: (1) 27 s (2) 4 s (3) 13 s (4) 7 s

Q11.When 100 g of a liquid A at 100∘C is added to 50 g of a liquid B at temperature 75∘C , the temperature of the mixture becomes 90∘C . The temperature of the mixture, if 100 g of liquid A at 100∘C is added to 50 g of liquid B at 50∘C , will be: (1) 85∘C (2) 60∘C (3) 80∘C (4) 70∘C

Q11.A cubical block of side 0.5 m floats on water with 30% of its volume under water. What is the maximum weight that can be put on the block without fully submerging it under water? [Take, density of water = 103 kg / m3 ] JEE Main 2019 (10 Apr Shift 2) JEE Main Previous Year Paper (1) 87.5 kg (2) 65.4 kg (3) 30.1 kg (4) 46.3 kg

Q11.A Carnot engine has an efficiency of 1 6 . When the temperature of the sink is reduced by 62 ℃ , its efficiency is doubled. The temperatures of the source and the sink are, respectively, JEE Main 2019 (12 Apr Shift 2) JEE Main Previous Year Paper (1) 124 ℃, 62 ℃ (2) 37 ℃, 99 ℃ (3) 99 ℃, 37 ℃ (4) 62 ℃, 124 ℃

Q11.A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T. Considering only translational and rotational modes, the total internal energy of the system is (1) 15RT (2) 12RT (3) 4RT (4) 20RT

Q11.Temperature difference of 120𝑜𝐶 is maintained between two ends of a uniform rod 𝐴𝐵 of length 2𝐿. Another 3𝐿 bent rod 𝑃𝑄, of same cross-section as 𝐴𝐵 and length , is connected across 𝐴𝐵 (See figure). In steady state, 2 temperature difference between 𝑃 and 𝑄 will be close to: (1) 45𝑜𝐶 (2) 35𝑜𝐶 (3) 60𝑜𝐶 (4) 75𝑜𝐶

Q11.Three Carnot engines operate in series between a heat source at a temperature T1 and a heat sink at temperature T4 (see figure). There are two other reservoirs at temperature T2 and T3, as shown, with JEE Main 2019 (10 Jan Shift 1) JEE Main Previous Year Paper T1 > T2 > T3 > T4. The three engines are equally efficient if: (1) 1 1 1 1 T2 = (T1T 42 ) 3 ; T3 = (T 12 T4) 3 (2) T2 = (T1T4) 2 ; T3 = (T 12 T4) 3 (3) 1 1 1 1 T2 = (T 12 T4) 3 ; T3 = (T1T 42 ) 3 (4) T2 = (T 13 T4) 4 ; T3 = (T1T 43 ) 3

Q11.Two moles of helium gas is mixed with three moles of hydrogen molecules (taken to be rigid). What is the molar specific heat of mixture at constant volume? R = 8.3 J / mol K (1) 17.4 J / mol K (2) 19.7 J / mol K (3) 15.7 J / mol K (4) 21.6 J / mol K

Q12.A train moves towards a stationary observer with speed 34 m/s. The train sounds a whistle and its frequency registered by the observer is f1. If the speed of the train is reduced to 17 m/s, the frequency registered is f2. If speed of sound is 340 m/s, then the ratio f1/f2 is: (1) 21/20 (2) 20/19 (3) 19/18 (4) 18/17

Q12.A simple harmonic motion is represented by: cm y = 3πt + √3 cos 3πt) 5(sin The amplitude and time period of the motion are: (1) 5 cm, 23 s (2) 10 cm, 23 s (3) 5 cm, 23 s (4) 10 cm, 32 s

Q12.A massless spring (k = 800 N/m), attached with a mass (500 g) is completely immersed in 1 kg of water. The spring is stretched by 2 cm and released so that it starts vibrating. What would be the order of magnitude of the change in the temperature of water when the vibrations stop completely? (Assume that the water container and spring receive negligible heat and specific heat of mass = 400 J/kg K, specific heat of water = 4184 J/kg K ) (1) 10−5 K (2) 10−1 K (3) 10−3 K (4) 10−4 K

Q12.The temperature, at which the root mean square velocity of hydrogen molecules equals their escape their escape velocity from the earth, is closest to: [ Boltzmann Constant kB = 1.38 × 10-23 J / K Avogadro number NA = 6.02 × 1026 / kg Radius of Earth: 6.4 × 106 m Gravitational acceleration on Earth = 10 ms-2] (1) 3 × 105K (2) 650 K (3) 800 K (4) 104 K JEE Main 2019 (08 Apr Shift 2) JEE Main Previous Year Paper

Q12.A rod of mass M and length 2L is suspended at its middle by a wire. It exhibits torsional oscillations. If two masses, each of mass m, are attached at a distance L/2 from its centre on both sides, it reduces the oscillation frequency by 20%. The value of ratio m/M is close to (1) 0.17 (2) 0.77 (3) 0.57 (4) 0.37

Q12.A hoop and a solid cylinder of same mass and radius are made of a permanent magnetic material with their respective axes. But the magnetic moment of hoop is twice of solid cylinder. They are placed in a uniform magnetic field in such a manner that their magnetic moments make a small angle with the field. If the oscillation periods of hoop and cylinder are Th and Tc respectively, then: (1) Th = 2Tc (2) Th = Tc (3) Th = 0.5Tc (4) Th = 1.5Tc