Practice Questions

Q9. The variation of kinetic energy (KE) of a particle executing simple harmonic motion with the displacement (𝑥) starting from mean position to extreme position (𝐴) is given by (1) (2) (3) (4)

Q9. Eight equal drops of water are falling through air with a steady speed of 10 cm s−1 . If the drops coalesce, the new velocity is:- (1) 16 cm s−1 (2) 40 cm s−1 (3) 5 cm s−1 (4) 10 cm s−1 JEE Main 2023 (11 Apr Shift 2) JEE Main Previous Year Paper

Q9. The mean free path of molecules of a certain gas at STP is 1500𝑑, where 𝑑 is the diameter of the gas molecules. While maintaining the standard pressure, the mean free path of the molecules at 373 𝐾 is approximately: JEE Main 2023 (13 Apr Shift 2) JEE Main Previous Year Paper (1) 750𝑑 (2) 1098𝑑 (3) 2049𝑑 (4) 1500𝑑

Q9. Surface tension of a soap bubble is 2. 0 × 10−2 N m−1 . Work done to increase the radius of soap bubble from 3. 5 cm to 7 cm will be : [Take π = 227 ] (1) 0. 72 × 10−4 J (2) 5. 76 × 10−4 J (3) 18. 48 × 10−4 J (4) 9. 24 × 10−4 J JEE Main 2023 (29 Jan Shift 1) JEE Main Previous Year Paper

Q9. The weight of a body on the earth is 400 N. Then weight of the body when taken to a depth half of the radius of the earth will be: (1) 200 N (2) Zero (3) 100 N (4) 300 N

Q9. If the distance of the earth from Sun is 1. 5 × 106 km, then the distance of an imaginary planet from Sun, if its period of revolution is 2. 83 years is: (1) 6 × 107 km (2) 6 × 106 km (3) 3 × 106 km (4) 3 × 107 km

Q9. A flask contains Hydrogen and Argon in the ratio 2 : 1 by mass. The temperature of the mixture is 30°C . The ratio of average kinetic energy per molecule of the two gases ( KhydrogenKargon ) is: (Given : Atomic Weight of Ar = 39. 9 ) (1) 2 (2) 1 (3) 39. 9 (4) 39.92

Q9. For a periodic motion represented by the equation 𝑦= sinω𝑡+ cosω𝑡 the amplitude of the motion is (1) 1 (2) 0 . 5 (3) 2 (4) √2

Q9. Under isothermal condition, the pressure of a gas is given by P = aV –3, where a is a constant and V is the volume of the gas. The bulk modulus at constant temperature is equal to (1) 3P (2) P (3) 2P (4) P2

Q9. The correct relation between 𝛾= and temperature 𝑇 is : 𝐶𝑉 (1) 𝛾∝ 1 (2) 𝛾∝𝑇0 √𝑇 (3) 𝛾∝1 (4) 𝛾∝𝑇 𝑇

Q9. The time period of a satellite of earth is 24 hours. If the separation between the earth and the satellite is decreased to one fourth of the previous value, then its new time period will become. (1) 4 hours (2) 6 hours (3) 12 hours (4) 3 hours

Q9. T is the time period of simple pendulum on the earth's surface. Its time period becomes xT when taken to a height R (equal to earth's radius) above the earth's surface. Then, the value of x will be: (1) 4 (2) 2 (3) 1 (4) 1 2 4

Q9. A hydraulic automobile lift is designed to lift vehicles of mass 5000 kg. The area of cross section of the cylinder carrying load is 250 cm2 . The maximum pressure the smaller piston would have to bear is [Assume g = 10 m s−2 ] (1) 20 × 106 Pa (2) 2 × 105 Pa (3) 200 × 106 Pa (4) 2 × 106 Pa

Q9. A metal block of mass m is suspended from a rigid support through a metal wire of diameter 14 mm. The tensile stress developed in the wire under equilibrium state is 7 × 105 N m–2 . The value of mass m is ______ kg. (Take g = 9. 8 m s−2 and π = 227 )

Q9. Every planet revolves around the sun in an elliptical orbit : A. The force acting on a planet is inversely proportional to square of distance from sun. B. Force acting on planet is inversely proportional to product of the masses of the planet and the sun. C. The centripetal force acting on the planet is directed away from the sun. D. The square of time period of revolution of planet around sun is directly proportional to cube of semi-major axis of elliptical orbit. Choose the correct answer from the options given below : (1) A and D only (2) C and D only (3) B and C only (4) A and C only

Q9. Under the same load, wire A having length 5. 0 m and cross section 2. 5 × 10−5 m2 stretches uniformly by the same amount as another wire B of length 6. 0 m and a cross section of 3. 0 × 10−5 m2 stretches. The ratio of the JEE Main 2023 (31 Jan Shift 2) JEE Main Previous Year Paper Young's modulus of wire A to that of wire B will be: (1) 1 : 4 (2) 1 : 1 (3) 1 : 10 (4) 1 : 2

Q9. For a body projected at an angle with the horizontal from the ground, choose the correct statement (1) Gravitational potential energy is maximum at the (2) The horizontal component of velocity is zero at highest point. highest point. (3) The vertical component of momentum is (4) The kinetic energy (K.E.) is zero at the highest maximum at the highest point. point of projectile motion.

Q9. Heat is given to an ideal gas in an isothermal process. A. Internal energy of the gas will decrease. B. Internal energy of the gas will increase. C. Internal energy of the gas will not change. D. The gas will do positive work. E. The gas will do negative work. Choose the correct answer from the options given below : (1) A and E only (2) B and D only (3) C and E only (4) C and D only

Q9. A travelling wave is described by the equation 𝑦𝑥, 𝑡= 0 . 05sin8𝑥- 4𝑡 m. The velocity of the wave is: [All the quantities are in SI unit] (1) 4 m s-1 (2) 2 m s-1 (3) 0 . 5 m s-1 (4) 8 m s-1

Q10.A faulty thermometer reads 5°C in melting ice and 95°C in steam. The correct temperature on absolute scale will be ______ K when the faulty thermometer reads 41°C.

Q10.An aluminium rod with Young’s modulus Y = 7. 0 × 1010 N m−2 undergoes elastic strain of 0. 04%. The energy per unit volume stored in the rod in SI unit JEE Main 2023 (08 Apr Shift 1) JEE Main Previous Year Paper (1) 2800 (2) 11200 (3) 5600 (4) 8400

Q10.Glycerin of density 1. 25 × 103 kg m–3 is flowing through the conical section of pipe. The area of cross- section of the pipe at its ends are 10 cm2 and 5 cm2 and pressure drop across its length is 3 N m–2 . The rate of flow of glycerine through the pipe is x × 10–5 m3 s–1 . The value of x is _____.

Q10.The electric field in an electromagnetic wave is given as →𝐸= 20sin𝜔𝑡- 𝑥 →jN C-1, where 𝜔 and 𝑐 are angular frequency and velocity of electromagnetic wave 𝑐 respectively. The energy contained in a volume of 5 × 10-4 m3 will be (Given 𝜀0 = 8 . 85 × 10-12C2 N-1 m-2) (1) 88 . 5 × 10-13 J (2) 17 . 7 × 10-13 J (3) 28 . 5 × 10-13 J (4) 8 . 85 × 10-13 J

Q10.A particle executes S.H.M. of amplitude 𝐴 along 𝑥-axis. At 𝑡= 0, the position of the particle is 𝑥= and it 2 moves along positive 𝑥-axis. The displacement of particle in time 𝑡 is 𝑥= 𝐴 sin𝜔𝑡 + 𝛿, then the value 𝛿 will be (1) 𝜋 (2) 𝜋 2 6 𝜋 𝜋 (3) (4) 3 4

Q10.A steel wire with mass per unit length 7 . 0 × 10 – 3 kg m – 1 is under tension of 70 N. The speed of transverse waves in the wire will be: (1) 200π m s-1 (2) 100 m s-1 (3) 10 m s-1 (4) 50 m s-1