Practice Questions

Q6. Correct formula for height of a satellite from earths surface is: JEE Main 2024 (04 Apr Shift 2) JEE Main Previous Year Paper (1) T 2R2 1/3 (2) T 2R2g 1/3 −R −R ( 4π2g ) ( 4π2 ) (3) T 2R2g −1/3 (4) T 2R2g 1/2 + R −R ( 4π2 ) ( 4π )

Q6. At what distance above and below the surface of the earth a body will have same weight? (Take radius of earth as R) (1) √5R −R (2) √3R−R 2 (3) R (4) √5R−R 2 2

Q6. A ball of mass 0 . 5 kg is attached to a string of length 50 cm. The ball is rotated on a horizontal circular path about its vertical axis. The maximum tension that the string can bear is 400 N. The maximum possible value of angular velocity of the ball in rad s-1 is,: (1) 1600 (2) 40 (3) 1000 (4) 20 JEE Main 2024 (01 Feb Shift 1) JEE Main Previous Year Paper

Q6. Ratio of radius of gyration of a hollow sphere to that of a solid cylinder of equal mass, for moment of Inertia about their diameter axis AB as shown in figure is √8/x. The value of x is : (1) 51 (2) 34 (3) 17 (4) 67 JEE Main 2024 (05 Apr Shift 1) JEE Main Previous Year Paper

Q6. A satellite revolving around a planet in stationary orbit has time period 6 hours. The mass of planet is one-fourth the mass of earth. The radius orbit of planet is : ( Given = Radius of geo-stationary orbit for earth is 4.2 × 104 km ) (1) 1.4 × 104 km (2) 1.05 × 104 km (3) 8.4 × 104 km (4) 1.68 × 105 km

Q6. An astronaut takes a ball of mass m from earth to space. He throws the ball into a circular orbit about earth at an altitude of 318.5 km. From earth's surface to the orbit, the change in total mechanical energy of the ball is x GMem . The value of x is (take Re = 6370 km) : 21Re (1) 10 (2) 12 (3) 9 (4) 11

Q6. The mass of the moon is times the mass of a planet and its diameter times the diameter of a planet. If the 144 16 escape velocity on the planet is v, the escape velocity on the moon will be: (1) 𝑣 (2) 𝑣 3 4 𝑣 𝑣 (3) (4) 12 6

Q6. A light planet is revolving around a massive star in a circular orbit of radius 𝑅 with a period of revolution 𝑇. If the force of attraction between planet and star is proportional to 𝑅-3 / 2 then choose the correct option : (1) 𝑇2 ∝𝑅5 / 2 (2) 𝑇2 ∝𝑅7 / 2 (3) 𝑇2 ∝𝑅3 / 2 (4) 𝑇2 ∝𝑅3

Q6. The gravitational potential at a point above the surface of earth is −5. 12 × 107 J kg−1 and the acceleration due to gravity at that point is 6. 4 m s−2 . Assume that the mean radius of earth to be 6400 km. The height of this point above the earth's surface is: (1) 1600 km (2) 540 km (3) 1200 km (4) 1000 km

Q7. A simple pendulum doing small oscillations at a place R height above earth surface has time period of T1 = 4 s . T2 would be it's time period if it is brought to a point which is at a height 2R from earth surface. Choose the correct relation [R = radius of earth ] : (1) 2 T1 = T2 (2) 2 T1 = 3 T2 (3) T1 = T2 (4) 3 T1 = 2 T2

Q7. A real gas within a closed chamber at 27∘C undergoes the cyclic process as shown in figure. The gas obeys PV 3 = RT equation for the path A to B. The net work done in the complete cycle is (assuming R = 8 J/molK JEE Main 2024 (09 Apr Shift 2) JEE Main Previous Year Paper ): (1) 20 J (2) 205 J (3) −20 J (4) 225 J

Q7. A big drop is formed by coalescing 1000 small droplets of water. The surface energy will become : JEE Main 2024 (01 Feb Shift 2) JEE Main Previous Year Paper (1) 100 times (2) 10 times 1 1 (3) 100th (4) 10th

Q7. A wire of length L and radius r is clamped at one end. If its other end is pulled by a force F , its length increases by l. If the radius of the wire and the applied force both are reduced to half of their original values keeping original length constant, the increase in length will become: (1) 3 times (2) 32 times (3) 4 times (4) 2 times

Q7. A cube of ice floats partly in water and partly in kerosene oil. The ratio of volume of ice immersed in water to that in kerosene oil (specific gravity of Kerosene oil = 0.8, specific gravity of ice = 0.9) JEE Main 2024 (08 Apr Shift 2) JEE Main Previous Year Paper (1) 1 : 1 (2) 5 : 4 (3) 8 : 9 (4) 9 : 10

Q7. An artillery piece of mass 𝑀1 fires a shell of mass 𝑀2 horizontally. Instantaneously after the firing, the ratio of kinetic energy of the artillery and that of the shell is : 𝑀1 𝑀2 (1) (2) ( 𝑀1 + 𝑀2 ) 𝑀1 (3) 𝑀2 (4) 𝑀1 ( 𝑀1 + 𝑀2 ) 𝑀2

Q7. A small spherical ball of radius 𝑟, falling through a viscous medium of negligible density has terminal velocity 𝑣. Another ball of the same mass but of radius 2𝑟, falling through the same viscous medium will have terminal velocity: (1) 𝑣 (2) 𝑣 2 4 (3) 4𝑣 (4) 2𝑣

Q7. If 𝑅 is the radius of the earth and the acceleration due to gravity on the surface of earth is 𝑔= 𝜋2 m s-2, then the length of the second's pendulum at a height ℎ= 2𝑅 from the surface of earth will be: 2 1 (1) m (2) m 9 9 (3) 4 m (4) 8 m 9 9

Q7.Match List-I with List-II : List-I List-II (A) A force that restores an elastic body of unit area to its original state (I) Bulk modulus (B) Two equal and opposite forces parallel to opposite faces (II) Young's modulus Forces perpendicular everywhere to the surface per unit area (C) (III) Stress same everywhere (D) Two equal and opposite forces perpendicular to opposite faces (IV) Shear modulus Choose the correct answer from the options given below : (1) (A)-(IV), (B)-(II), (C)-(III), (D)-(I) (2) (A)-(III), (B)-(IV), (C)-(I), (D)-(II) (3) (A)-(II), (B)-(IV), (C)-(I), (D)-(III) (4) (A)-(III), (B)-(I), (C)-(II), (D)-(IV)

Q7. A sphere of relative density σ and diameter D has concentric cavity of diameter d. The ratio of Dd , if it just floats on water in a tank is : (1) ( σ+2σ−2 ) 1/3 (2) ( σ−1σ )1/3 (3) σ−1 1/3 (4) σ+1 1/3 ( σ ) ( σ−1 )

Q7. To project a body of mass m from earth's surface to infinity, the required kinetic energy is (assume, the radius of earth is RE, g = acceleration due to gravity on the surface of earth): (1) 2mgRE (2) 4mgRE (3) mgRE (4) 1/2mgRE

Q8. During an adiabatic process, if the pressure of a gas is found to be proportional to the cube of its absolute temperature, then the ratio of CP for the gas is : CV JEE Main 2024 (05 Apr Shift 2) JEE Main Previous Year Paper (1) 5 (2) 9 3 7 (3) 3 (4) 7 2 5

Q8. In hydrogen like system the ratio of coul0mbian force and gravitational force between an electron and a proton is in the order of : (1) 1039 (2) 1029 (3) 1019 (4) 1036

Q8. A small ball of mass m and density ρ is dropped in a viscous liquid of density ρ0 . After sometime, the ball falls with constant velocity. The viscous force on the ball is : JEE Main 2024 (06 Apr Shift 1) JEE Main Previous Year Paper (1) mg (1 −ρρ0) (2) mg (1 + ρ0ρ ) (3) mg ( ρ0ρ −1) (4) mg(1 −ρ0ρ ) ∇

Q8. A sample of gas at temperature T is adiabatically expanded to double its volume. Adiabatic constant for the gas is γ = 3/2. The work done by the gas in the process is: (μ = 1 mole) (1) RT[1 −2√2] (2) RT[√2 −2] (3) RT[2 −√2] (4) RT[2√2 −1]

Q8. A total of 48 J heat is given to one mole of helium kept in a cylinder. The temperature of helium increases by 2∘C. The work done by the gas is: Given, R = 8.3 J K−1 mol−1 . JEE Main 2024 (06 Apr Shift 2) JEE Main Previous Year Paper (1) 24.9 J (2) 72.9 J (3) 48 J (4) 23.1 J