Practice Questions

Q5. In the given arrangement of a doubly inclined plane two blocks of masses 𝑀 and 𝑚 are placed. The blocks are connected by a light string passing over an ideal pulley as shown. The coefficient of friction between the surface of the plane and the blocks is 0 . 25. The value of 𝑚, for which 𝑀= 10 kg will move down with an 3 acceleration of 2 m s-2, is: (take 𝑔= 10 m s-2 and tan 37° = 4) (1) 9 kg (2) 4 . 5 kg (3) 6 . 5 kg (4) 2 . 25 kg

Q5. A body of mass 2 kg begins to move under the action of a time dependent force given by → 𝐹= 6𝑡 ^i + 6𝑡2 ^j N. The power developed by the force at the time 𝑡 is given by: (1) 6𝑡4 + 9𝑡5 W (2) 3𝑡3 + 6𝑡5 W (3) 9𝑡5 + 6𝑡3 W (4) 9𝑡3 + 6𝑡5 W JEE Main 2024 (31 Jan Shift 2) JEE Main Previous Year Paper 1 1

Q5. A body of mass 1000 kg is moving horizontally with a velocity 6 m s−1 . If 200 kg extra mass is added, the final velocity (in m s−1 ) is: (1) 6 (2) 2 (3) 3 (4) 5

Q5. The potential energy function (in J ) of a particle in a region of space is given as U = (2x2 + 3y3 + 2z). Here x, y and z are in meter. The magnitude of x - component of force (in N ) acting on the particle at point P(1, 2, 3) m is: (1) 2 (2) 6 (3) 4 (4) 8

Q5. A spherical body of mass 100 g is dropped from a height of 10 m from the ground. After hitting the ground, the body rebounds to a height of 5 m . The impulse of force imparted by the ground to the body is given by: (given g = 9. 8 m s−2 ) (1) 4. 32 kg m s−1 (2) 43. 2 kg m s−1 (3) 23. 9 kg m s−1 (4) 2. 39 kg m s−1 JEE Main 2024 (30 Jan Shift 1) JEE Main Previous Year Paper

Q5. A wooden block, initially at rest on the ground, is pushed by a force which increases linearly with time t. Which of the following curve best describes acceleration of the block with time: (1) (2) (3) (4)

Q5. A 90 kg body placed at 2R distance from surface of earth experiences gravitational pull of : ( R = Radius of earth, g = 10 m s−2 ) (1) 100 N (2) 300 N (3) 225 N (4) 120 N

Q5. A simple pendulum of length 1 m has a wooden bob of mass 1 kg. It is struck by a bullet of mass 10-2 kg moving with a speed of 2 × 102 m s-1. The bullet gets embedded into the bob. The height to which the bob rises before swinging back is. (use 𝑔= 10 m s-2) (1) 0 . 30 m (2) 0 . 20 m (3) 0 . 35 m (4) 0 . 40 m

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. Two satellite A and B go round a planet in circular orbits having radii 4R and R respectively. If the speed of A is 3v, the speed of B will be : (1) 3v (2) 6v (3) 4 v (4) 12v 3

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. Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : The angular speed of the moon in its orbit about the earth is more than the angular speed of the earth in its orbit about the sun. Reason (R): The moon takes less time to move around the earth than the time taken by the earth to move around the sun. In the light of the above statements, choose the most appropriate answer from the options given below : (1) (A) is correct but (R) is not correct (2) Both (A) and (R) are correct and (R) is the correct explanation of A. (3) Both (A) and (R) are correct but (R) is not the (4) (A) is not correct but (R) is correct correct explanation of A.

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. 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 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. 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. 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 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. 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. 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. 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

Q6. Four particles A, B, C, D of mass m2 , m, 2m, 4m, have same momentum, respectively. The particle with maximum kinetic energy is : (1) B (2) A (3) D (4) C

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. 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