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.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

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.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 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

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 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.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 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 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.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 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 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

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 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

Q14.A positive point charge is released from rest at a distance r0 from a positive line charge with uniform charge density. The speed ( v ) of the point charge, as a function of instantaneous distance r from line charge, is proportional to (1) v ∝r (2) v r r0 ∝√ln⁡r0 +r (3) v ∝ln⁡r (4) r0 v ∝e r0

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.Figure shows charge (q) versus voltage (V) graph for series and parallel combination of two given capacitors. The capacitances are: (1) 60 μF and 40 μF (2) 50 μF and 30 μF (3) 20 μF and 30 μF (4) 40 μF and 10 μF

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 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.A cylindrical plastic bottle of negligible mass is filled with 310 ml of water and left floating in a pond with still water. If pressed downward slightly and released, it starts performing simple harmonic motion at angular frequency ω. If the radius of the bottle is 2.5 cm then ω is close to: ( density of water = 103kg/m3) (1) 5.00 rad sec−1 (2) 2.50 rad sec−1 (3) 7.9 rad sec−1 (4) 3.75 rad sec−1

Q14.Three charges +𝑄, 𝑞, + 𝑄 are placed respectively, at distance, 0, 𝑑/ 2 and 𝑑 from the origin, on the 𝑥 -axis. If the net force experienced by +𝑄, placed at 𝑥= 0, is zero, then value of 𝑞 is: (1) +𝑄/ 2 (2) +𝑄/ 4 (3) -𝑄/ 4 (4) -𝑄/ 2

Q15.Two sources of sound S1 and S2 produce sound waves of same frequency 660 Hz. A listener is moving from source S1 towards S2 with a constant speed u0 m/s and he hears 10 beats/s. The velocity of sound is 330 m/s. Then, u0 equals: (1) 10.0 m/s (2) 2.5 m/s (3) 5.5 m/s (4) 15.0 m/s

Q15.In the circuit shown, find C if the effective capacitance of the whole circuit is to be 0.5 μF. All values in the circuit are in μF. JEE Main 2019 (12 Jan Shift 2) JEE Main Previous Year Paper (1) 7 μF (2) 4μF 10 (3) 7 μF (4) 6 μF 11 5

Q15.A Point dipole →p = - p0^𝑥 at a distance d are, respectively: (Taken V = 0 at infinity) | (1) |→p | -→p (2) |→p 4πε0d2, 4πε0d3 0, 4πε0d3 -→p (3) |→p | →p (4) 4πε0d3 4πε0d3, 4πε0d3 0,