Practice Questions

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 metal ball of mass 0.1 kg is heated upto 500∘C and dropped into a vessel of heat capacity 800JK−1 and containing 0.5 kg water. The initial temperature of water and vessel is 30∘C . What is the approximate percentage increment in the temperature of the water? [Specific Heat Capacities of water and metal are, respectively, 4200Jkg−1 K−1 and 400Jkg−1 K−1 ] (1) 15% (2) 30% (3) 25% (4) 20%

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

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 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.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 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.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 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.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.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.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 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.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.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

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 simple pendulum oscillating in air has period T . The bob of the pendulum is completely immersed in a non- viscous liquid. The density of the liquid is 161 th of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is: (1) 2T√110 (2) 2T√114 (3) 4T√115 (4) 4T√114

Q14.Two electric dipoles, A, B with respective dipole moments dA→ = −4qaˆi and dB→ = −2qaˆi are placed on the x - axis with a separation R, as shown in the figure The distance from A at which both of them produce the same potential is: (1) R (2) √2R √2 −1 √2−1 (3) √2 R (4) R √2+1 √2+1 JEE Main 2019 (10 Jan Shift 1) JEE Main Previous Year Paper

Q14.The bob of a simple pendulum has mass 2 g and a charge of 5.0 μC . It is at rest in a uniform horizontal electric field of intensity 2000 V / m At equilibrium, the angle that the pendulum makes with the vertical is: take g = 10 m / s2 (1) tan-10.2 (2) tan-12.0 (3) tan-10.5 (4) tan-15.0

Q14.A string 2.0 m long and fixed at its ends is driven by a 240 Hz vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is (1) 320 m s−1, 120 Hz (2) 320 m s−1, 80 Hz (3) 180 m s−1, 80 Hz (4) 180 m s−1, 120 Hz

Q14.The given graph shows variation (with distancer from centre) of: (1) Electric field of a uniformly charged sphere (2) Potential of a uniformly charged spherical shell (3) Potential of a uniformly charged sphere (4) Electric field of a uniformly charged spherical shell

Q14.One mole of an ideal gas passes through a process where pressure and volume obey the relation 1 Vo 2 P = Po1 - . Here Po and Vo are constants. Calculate the change in the temperature of the gas if its volume 2 V changes from Vo to 2Vo . 1 P0V0 5 P0V0 (1) (2) 4 R 4 R 1 P0V0 3 P0V0 (3) (4) 2 R 4 R

Q14.A parallel plate capacitor with plates of area 1 m2 each, are at a separation of 0.1 m. If the electric field between the plates is 100 N/C, the magnitude of charge on each plate is: (Take ∈0= 8.85 × 10−12 N-m2C 2 ) (1) 8.85 x 10−10C (2) 6.85 x 10−10C (3) 9.85 x 10−10C (4) 7.85 x 10−10C

Q14.A small speaker delivers 2 W of audio output. At what distance from the speaker will one detect 120 dB intensity sound? [Given reference intensity of sound as 10−12 W/m2 ] (1) 40 cm (2) 20 cm (3) 10 cm (4) 30 cm

Q14.A string is clamped at both the ends and it is vibrating in its 4th harmonic. The equation of the stationary wave is y = 0.3 sin(0.157x) cos(200πt). The length of the string is JEE Main 2019 (09 Apr Shift 1) JEE Main Previous Year Paper (All quantities are in SI units.) (1) 20 m (2) 60 m (3) 40 m (4) 80 m