Practice Questions

Q6. A coin is placed on a disc. The coefficient of friction between the coin and the disc is 𝜇. If the distance of the coin from the center of the disc is 𝑟, the maximum angular velocity which can be given to the disc, so that the coin does not slip away, is : JEE Main 2024 (31 Jan Shift 1) JEE Main Previous Year Paper 𝜇𝑔 𝑟 (1) (2) 𝑟 √ 𝜇𝑔 𝜇𝑔 𝜇 (3) (4) √ 𝑟 √𝑟𝑔

Q6. A spherical ball of radius 1 × 10−4 m and density 105 kg/m3 falls freely under gravity through a distance h before entering a tank of water, If after entering in water the velocity of the ball does not change, then the value of h is approximately: (The coefficient of viscosity of water is 9.8 × 10−6 N s/m2 ) (1) 2296 m (2) 2518 m (3) 2249 m (4) 2396 m

Q6. Escape velocity of a body from earth is 11 . 2 km s-1. If the radius of a planet be one-third the radius of earth and mass be one-sixth that of earth, the escape velocity from the plate is: (1) 11 . 2 km s-1 (2) 8 . 4 km s-1 (3) 4 . 2 km s-1 (4) 7 . 9 km s-1

Q6. The acceleration due to gravity on the surface of earth is g. If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be : (1) g (2) 2g 4 (3) g (4) 4g 2

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. 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

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. 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. If a rubber ball falls from a height h and rebounds upto the height of h/2. The percentage loss of total energy of the initial system as well as velocity ball before it strikes the ground, respectively, are : (1) 50%, √2gh (2) 50%, √gh (3) 40%, √2gh (4) 50%, √gh2 JEE Main 2024 (04 Apr Shift 1) JEE Main Previous Year Paper

Q6. Assuming the earth to be a sphere of uniform mass density, a body weighed 300 N on the surface of earth. How much it would weigh at R/4 depth under surface of earth ? (1) 75 N (2) 300 N (3) 375 N (4) 225 N

Q6. A planet takes 200 days to complete one revolution around the Sun. If the distance of the planet from Sun is reduced to one fourth of the original distance, how many days will it take to complete one revolution? (1) 25 (2) 50 (3) 100 (4) 20 JEE Main 2024 (29 Jan Shift 2) JEE Main Previous Year Paper

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. 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

Q7. Young's modules of material of a wire of length L and cross-sectional area A is Y . If the length of the wire is doubled and cross-sectional area is halved then Young's modules will be: (1) Y (2) 4Y 4 (3) Y (4) 2Y

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. 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. Two planets A and B having masses m1 and m2 move around the sun in circular orbits of r1 and r2 radii respectively. If angular momentum of A is L and that of B is 3 L, the ratio of time period ( TBTA ) is: (1) r2 32 (2) 1 m2 3 27 ( m1 ) ( r1 ) (3) m1 3 (4) r1 3 27( m2 ) ( r2 )

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 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 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.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 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. A metal wire of uniform mass density having length L and mass M is bent to form a semicircular arc and a particle of mass m is placed at the centre of the arc. The gravitational force on the particle by the wire is : (1) GmMπ2 (2) GMmπ L2 2 L2 (3) 0 (4) 2GmMπ L2

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. 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