Practice Questions

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 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 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

Q12.Two identical beakers A and B contain equal volumes of two different liquids at 60°C each and left to cool down. Liquid in A has density of 8 × 102 kg m-3 and specific heat of 2000 J kg-1K-1 while the liquid in B has density 103 kg m-3 and specific heat of 4000 J kg-1K-1. Which of the following best describes their temperature versus time graph schematically? (assume the emissivity of both the beakers to be the same) (1) (2) (3) (4)

Q12.An HCl molecule has rotational, translational and vibrational motions. If the rms velocity of HCl molecules in − its gaseous phase is ν , m is its mass and kB is Boltzmann's constant, then its temperature will be: (1) m−ν 2 (2) m−ν 2 5kB 6kB (3) m−ν 2 (4) m−ν 2 3kB 7kB

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 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.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 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

Q13.A progressive wave travelling along the positive 𝑥- direction is represented by 𝑦𝑥, t = A sin ( k𝑥- ωt + ϕ ) . Its snapshot at t = 0 is given in the figure. For this wave, the phase ϕ is: π (1) (2) 0 2 (3) π (4) -π 2

Q13.Equation of travelling wave on a stretched string of linear density 5 g/m is y = 0.03 sin(450t −9x) where distance and time are measured in SI units. The tension in the string is: (1) 10 N (2) 7.5 N (3) 12.5 N (4) 5 N

Q13.A pendulum is executing simple harmonic motion and its maximum kinetic energy is K1 . If the length of the pendulum is doubled and it performs simple harmonic motion with the same amplitude as in the first case, its maximum kinetic energy is K2 JEE Main 2019 (11 Jan Shift 2) JEE Main Previous Year Paper (1) K2 = 2K1 (2) K2 = K12 (3) K2 = K14 (4) K2 = K

Q13.A resonance tube is old and has a jagged end. It is still used in the laboratory to determine the velocity of sound in air. A tuning fork of frequency 512 Hz produces first resonance when the tube is filled with water to a mark 11 cm below a reference mark, near the open end of the tube. The experiment is repeated with another fork of frequency 256 Hz which produces first resonance when water reaches a mark 27 cm below the reference mark. The velocity of sound in air, obtained in the experiment, is close to (1) 335 m s−1 (2) 341 m s−1 (3) 322 m s−1 (4) 328 m s−1

Q13.A uniformly charged ring of radius 3a and total charge q is placed in x‐y plane centred at origin. A point charge q is moving towards the ring along the z− axis and has speed v at z = 4a . The minimum value of v such that it crosses the origin is: JEE Main 2019 (10 Apr Shift 1) JEE Main Previous Year Paper (1) √2m ( 151 4πϵ0aq2 ) 1/2 (2) √2m ( 154 4πϵ0aq2 ) 1/2 (3) √2m ( 51 4πϵ0aq2 ) 1/2 (4) √2m ( 152 4πϵ0aq2 ) 1/2

Q13.Determine the electric dipole moment of the system of three charges, placed on the vertices of an equilateral triangle, as shown in the figure: (1) √3 ql ˆj−ˆi (2) −√3 qlˆj √2 (3) 2 ql ˆj (4) (ql) ˆi+ˆj √2

Q13.A musician using an open flute of length 50 cm produces second harmonic sound waves. A person runs towards the musician from another end of a hall at a speed of 10 km h−1 . If the wave speed is 330 m s−1 , the frequency heard by the running person shall be close to (1) 333 Hz (2) 500 Hz (3) 666 Hz (4) 753 Hz JEE Main 2019 (09 Jan Shift 2) JEE Main Previous Year Paper

Q13.A submarine experiences a pressure of 5.05 × 106 Pa at a depth of d1 in a sea. When it goes further to a depth of d2 , it experiences a pressure of 8.08 × 106 Pa . Then d2 - d1 is approximately (density of water = 103 kg / m3 and acceleration due to gravity = 10 ms-2 ): (1) 600 m (2) 500 m (3) 300 m (4) 400 m

Q13.A string of length 1 m and mass 5 g is fixed at both ends. The tension in the string is 8 .0 N . The string is set into vibration using an external vibrator of frequency 100 Hz. The separation between successive nodes on the string is close to (1) 20. 0 cm (2) 10. 0 cm (3) 16 .6 cm (4) 33. 3 cm −−

Q13.A damped harmonic oscillator has a frequency of 5 oscillations per second. The amplitude drops to half its 1 value for every 10 oscillations. The time it will take to drop to of the original amplitude is close to: 1000 (1) 50 s (2) 100 s (3) 20 s (4) 10 s

Q13.The number density of molecules of a gas depends on their distance r from the origin as, n(r) = n0e−αr4. Then the numer of molecules is proportional to: 2 (1) n0α−3 (2) √n0α 1 4 (3) n0α −3 1 4 (4) n0α

Q13.Two cars A and B are moving away from each other in opposite directions. Both the cars are moving with speed of 20 m s−1 with respect to the ground. If an observer in car A detects a frequency 2000 Hz of the sound coming from car B, what is the natural frequency of the sound source in car B? (speed of sound in air = 340 m s−1 ) (1) 2150 Hz (2) 2300 Hz (3) 2250 Hz (4) 2060 Hz

Q13.A wire of length 2L, is made by joining two wires A and B of same length but different radii r and 2r and made of the same material. It is vibrating at a frequency such that the joint of the two wires forms a node. If JEE Main 2019 (08 Apr Shift 1) JEE Main Previous Year Paper the number of antinodes in wire A is p and that in B is q then ratio p: q is: (1) 3 : 5 (2) 4 : 9 (3) 1 : 4 (4) 1 : 2

Q13.A particle executes simple harmonic motion with an amplitude of 5 cm . When the particle is at 4 cm from the mean position, the magnitude of its velocity in SI units is equal to that of its acceleration. Then, its periodic time in seconds is: (1) 8π (2) 3 π 3 8 (3) 4π (4) 7 π 3 3

Q13.A mixture of 2 moles of helium gas (atomic mass = 4u) , and 1 mole of argon gas (atomic mass = 40 u) is kept 𝑉𝑟𝑚𝑠ℎ𝑒𝑙𝑖𝑢𝑚 at 300 𝐾 in a container. The ratio of their rms speeds , is close to: 𝑉𝑟𝑚𝑠( 𝑎𝑟𝑔𝑜𝑛) (1) 0.45 (2) 2.24 (3) 0.32 (4) 3.16