Practice Questions

Q4. A particle of mass m moves on a straight line with its velocity increasing with distance according to the equation v = α√x, where α is a constant. The total work done by all the forces applied on the particle during its displacement from x = 0 to x = d, will be : (1) m (2) md 2α2 d 2α2 (3) 2 mα2 d (4) mα22 d

Q4. A body of m kg slides from rest along the curve of vertical circle from point A to B in friction less path. The velocity of the body at B is: (given, R = 14 m, g = 10 m/s2 and √2 = 1.4 ) (1) 16.7 m/s (2) 19.8 m/s (3) 10.6 m/s (4) 21.9 m/s

Q4. The co-ordinates of a particle moving in x −y plane are given by : x = 2 + 4t, y = 3t + 8t2 . The motion of the particle is : (1) uniformly accelerated having motion along a (2) uniform motion along a straight line. parabolic path. (3) uniformly accelerated having motion along a (4) non-uniformly accelerated. straight line.

Q4. A block of mass 𝑚 is placed on a surface having vertical cross section given by 𝑦= 𝑥2 . If coefficient of friction 4 is 0 . 5, the maximum height above the ground at which block can be placed without slipping is: 1 1 (1) m (2) m 4 2 (3) 1 m (4) 1 m 6 3

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 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 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 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 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 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 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 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. 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 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 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 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

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. 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. 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. 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