Practice Questions

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. A body is moving unidirectionally under the influence of a constant power source. Its displacement in time t is proportional to : (1) t (2) t3/2 (3) t2 (4) t2/3

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 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 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 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. 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 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. 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. 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 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

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. 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. 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

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. 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 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. 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. 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

Q7. Given below are two statements: Statement I : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in hot water. Statement II : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in cold water. In the light of the above statements, choose the most appropriate from the options given below (1) Both Statement I and Statement II are true (2) Both Statement I and Statement II are false (3) Statement I is true but Statement II is false (4) Statement I is false but Statement II is true

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. 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