Practice Questions

Q10.In an experiment, brass and steel wires of length 1 m each with areas of cross section 1 mm2 are used. The wires are connected in series and one end of the combined wire is connected to a rigid support and other end is subjected to elongation. The stress required to produce a net elongation of 0.2 mm is, [Given, the Young's Modulus for steel and brass are, respectively, 120 × 109 N / m2 and 60 × 109 N / m2 ] (1) 8.0 × 106 N / m2 (2) 1.2 × 106 N / m2 (3) 0.2 × 106 N / m2 (4) 1.8 × 106 N / m2

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 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.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.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.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 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

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 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.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.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.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.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.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

Q12.A travelling harmonic wave is represented by the equation y(x, t) = 10−3 sin(50t + 2x), where x and y are in meter and t is in seconds. Which of the following is a correct statement about the wave? JEE Main 2019 (12 Jan Shift 1) JEE Main Previous Year Paper (1) The wave is propagating along the positive x - (2) The wave is propagating along the positive x - axis with speed 25 m s−1 axis with speed 100 m s−1 (3) The wave is propagating along the negative x - (4) The wave is propagating along the negative x - axis with speed 25 m s−1 axis with speed 100 m s−1

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.A particle undergoing simple harmonic motion has time dependent displacement given by x(t) = A sin 90πt . The ratio of kinetic to potential energy of this particle at t = 210 s will be (1) 1 (2) 1 9 (3) 2 (4) 1 3 JEE Main 2019 (11 Jan Shift 1) JEE Main Previous Year Paper

Q12.Water from a tap emerges vertically downwards with an initial speed of 1.0 ms-1 . The cross - sectional area of the tap is 10-4 m2 . Assume that the pressure is constant throughout the stream of water and that the flow is streamlined. The cross - sectional area of the stream, 0.15 m below the tap would be: (Take g = 10 ms-2 ) (1) 1 × 10-5 m2 (2) 5 × 10-4 m2 (3) 2 × 10-5 m2 (4) 5 × 10-5 m2

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 stationary source emits sound waves of frequency 500 Hz . Two observers moving along a line passing through the source detect sound to be of frequencies 480 Hz and 530 Hz . Their respective speeds are, in m s−1 , (Given speed of sound = 300 m/s ) (1) 16, 14 (2) 12, 16 (3) 12, 18 (4) 8, 18

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

Q12.A submarine A travelling at 18km hr-1 is being chased along the line of its velocity by another submarine B travelling at 27 km hr-1 . B sends a sonar signal of 500 Hz to detect A and receives a reflected sound of frequency v. The value of v is closed to (Speed of sound in water 1500 m s-1 ) (1) 504 Hz (2) 499 Hz (3) 502 Hz (4) 507 Hz

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 gas can be taken from A to B via two different processes ACB and ADB. When path ACB is used 60 J of heat flows into the system and 30 J of work is done by the system. If the path ADB is used then work done by the system is 10 J, the heat flows into the system in the path ADB is: (1) 100 J (2) 20 J (3) 40 J (4) 80 𝐽

Q12.A diatomic gas with rigid molecules does 10 J of work when expanded at constant pressure. What would be the heat energy absorbed by the gas, in this process? (1) 40 J (2) 35 J (3) 25 J (4) 30 J