Practice Questions

Q5. A heavy iron bar of weight 12 kg is having its one end on the ground and the other on the shoulder of a man. The rod makes an angle 60° with the horizontal, the normal force applied by the man on bar is: (1) 6 kg - wt (2) 12 kg - wt (3) 3 kg - wt (4) 6√3 kg - wt

Q5. When kinetic energy of a body becomes 36 times of its original value, the percentage increase in the momentum of the body will be: (1) 6% (2) 600% (3) 60% (4) 500%

Q5. A bob of mass m is suspended by a light string of length L. It is imparted a minimum horizontal velocity at the lowest point A such that it just completes half circle reaching the top most position B. The ratio of kinetic energies ( K.E. )A is : ( K.E. )B (1) 3 : 2 (2) 5 : 1 (3) 2 : 5 (4) 1 : 5

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 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 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. Three bodies A, B and C have equal kinetic energies and their masses are 400 g. 1.2 kg and 1.6 kg respectively. The ratio of their linear momenta is : (1) √2; √3; 1 (2) 1 : √3 : 2 (3) 1 : √3 : √2 (4) √3 : √2 : 1

Q5. A block is simply released from the top of an inclined plane as shown in the figure above. The maximum compression in the spring when the block hits the spring is : (1) √6 m (2) √5 m (3) 1 m (4) 2 m

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 heavy iron bar, of weight W is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle θ with the horizontal. The weight experienced by the person is : (1) W cos θ (2) W2 (3) W (4) W sin θ

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

Q5. The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is: (1) 1 : 9 (2) 1 : 3 (3) 1 : 27 (4) 1 : 81

Q5. A disc of radius 𝑅 and mass 𝑀 is rolling horizontally without slipping with speed 𝑣. It then moves up an inclined smooth surface as shown in figure. The maximum height that the disc can go up the incline is: (1) 𝑣2 (2) 3 𝑣2 𝑔 4 𝑔 (3) 1 𝑣2 (4) 2 𝑣2 2 𝑔 3 g

Q5. A block of mass 1 kg is pushed up a surface inclined to horizontal at an angle of 60° by a force of 10 N parallel to the inclined surface as shown in figure. When the block is pushed up by 10 m along inclined surface, the work done against frictional force is : 𝑔= 10 m s-2 (1) 5√3 J (2) 5 J (3) 5 × 103 J (4) 10 J

Q5. A bullet of mass 50 g is fired with a speed 100 m/s on a plywood and emerges with 40 m/s. The percentage loss of kinetic energy is : (1) 84% (2) 16% (3) 32% (4) 44%

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

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. 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. 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. 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. 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 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