Practice Questions

Q5. At any instant the velocity of a particle of mass 500 g is (2t ˆi + 3t2 ˆj) + x N . Then the value of x will be: particle at t = 1 s is (ˆi ˆj) (1) 3 (2) 4 (3) 2 (4) 6

Q5. A ball of mass 200 g rests on a vertical post of height 20 m. A bullet of mass 10 g, travelling in horizontal direction, hits the centre of the ball. After collision both travels independently. The ball hits the ground at a distance 30 m and the bullet at a distance of 120 m from the foot of the post. The value of initial velocity of the bullet will be (if 𝑔= 10 m s-2) : (1) 120 m s-1 (2) 60 m s-1 (3) 400 m s-1 (4) 360 m s-1 𝐾

Q5. A body of mass 5 kg is moving with a momentum of 10 kg m s−1 . Now a force of 2 N acts on the body in the direction of its motion for 5 s. The increase in the Kinetic energy of the body is _____ J.

Q5. The time period of a satellite, revolving above earth's surface at a height equal to R will be (Given 𝑔= 𝜋2 m s-2, 𝑅= radius of earth) (1) √2R (2) √8R (3) √32R (4) √4R

Q6. For rolling spherical shell, the ratio of rotational kinetic energy and total kinetic energy is x . The value of x is 5 _____.

Q6. Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth 𝑑= 𝑅 from the 2 surface of earth, if its weight on the surface of earth is 200 N, will be : (Given 𝑅= radius of earth) (1) 300 N (2) 100 N (3) 400 N (4) 500 N

Q6. Spherical insulating ball and a spherical metallic ball of same size and mass are dropped from the same height. Choose the correct statement out of the following {Assume negligible air friction} (1) Time taken by them to reach the earth's surface (2) Insulating ball will reach the earth's surface will be independent of the properties of their earlier than the metal ball materials (3) Both will reach the earth's surface simultaneously (4) Metal ball will reach the earth's surface earlier than the insulating ball

Q6. A body of mass 1 kg collides head on elastically with a stationary body of mass 3 kg. After collision, the smaller body reverses its direction of motion and moves with a speed of 2 m s−1 . The initial speed of the smaller body before collision is ______ m s−1 . JEE Main 2023 (25 Jan Shift 2) JEE Main Previous Year Paper

Q6. A ring and a solid sphere rotating about an axis passing through their centres have same radii of gyration. The axis of rotation is perpendicular to plane of ring. The ratio of radius of ring to that of sphere is . The value √2x of x is _____.

Q6. Given below are two statements : Statement-I: Acceleration due to gravity is different at different places on the surface of earth. Statement-II: Acceleration due to gravity increases as we go down below the earth's surface. In the light of the above statements, choose the correct answer 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

Q6. A hollow spherical ball of uniform density rolls up a curved surface with an initial velocity 3 m s−1 (as shown in figure). Maximum height with respect to the initial position covered by it will be _____ cm (take, g = 10 m s−2 ) JEE Main 2023 (08 Apr Shift 2) JEE Main Previous Year Paper

Q6. A ball is dropped from a height of 20 m. If the coefficient of restitution for the collision between ball and floor is 0. 5 , after hitting the floor, the ball rebounds to a height of ______ m.

Q6. The time taken by an object to slide down 45° rough inclined plane is n times as it takes to slide down a perfectly smooth 45° incline plane. The coefficient of kinetic friction between the object and the incline plane is: − n2 (1) √ 1−n21 (2) √1 1 (3) 1 + 1 (4) 1 − 1 n2 n2

Q6. A body of mass 2 kg is initially at rest. It starts moving unidirectionally under the influence of a source of constant power P . Its displacement in 4 s is 31 α2√P m. The value of α will be ______. JEE Main 2023 (30 Jan Shift 2) JEE Main Previous Year Paper

Q6. Given below are two statements: Statement I : For a planet, if the ratio of mass of the planet to its radius increase, the escape velocity from the planet also increase. Statement II : Escape velocity is independent of the radius of the planet. In the light of above statements, choose the most appropriate answer from the options given below (1) Statement I is incorrect but Statement II is correct (2) Statement I is correct but statement II is incorrect (3) Both Statement I and Statement II are incorrect (4) Both Statement I and Statement II are correct

Q6. Two identical particles each of mass m go round a circle of radius a under the action of their mutual gravitational attraction. The angular speed of each particle will be : (1) √Gma3 (2) √Gm8a3 (3) √Gm4a3 (4) √Gm2a3

Q6. A bullet of 10 g leaves the barrel of gun with a velocity of 600 m s−1 . If the barrel of gun is 50 cm long and mass of gun is 3 kg, then value of impulse supplied to the gun will be: (1) 6 N s (2) 3 N s (3) 36 N s (4) 12 N s

Q6. An object of mass 8 kg is hanging from one end of a uniform rod CD of mass 2 kg and length 1 m pivoted at its end C on a vertical wall as shown in figure. It is supported by a cable AB such that the system is in equilibrium. The tension in the cable is: (Take g = 10 m s−2 ) JEE Main 2023 (25 Jan Shift 1) JEE Main Previous Year Paper (1) 240 N (2) 90 N (3) 300 N (4) 30 N

Q6. A planet has double the mass of the earth. Its average density is equal to that of the earth. An object weighing 𝑊 on earth will weigh on that planet: (1) 1 (2) 1 2 4W 2 3W (3) 2W (4) 2 23W

Q6. A 100 m long wire having cross-sectional area 6 . 25 × 10-4 m2 and Young's modulus is 1010 N m-2 is subjected to a load of 250 N, then the elongation in the wire will be : (1) 6 . 25 × 10-3 m (2) 4 × 10-4 m (3) 6 . 25 × 10-6 m (4) 4 × 10-3 m Q7. 1 g of a liquid is converted to vapour at 3 × 105 Pa pressure. If 10% of the heat supplied is used for increasing the volume by 1600 cm3 during this phase change, then the increase in internal energy in the process will be : (1) 4320 J (2) 432000 J (3) 4800 J (4) 4 . 32 × 108 J JEE Main 2023 (24 Jan Shift 1) JEE Main Previous Year Paper

Q6. A 0. 4 kg mass takes 8 s to reach ground when dropped from a certain height P above surface of earth. The loss of potential energy in the last second of fall is ______ J. [Take g = 10 m s−2 ]

Q6. Figures (a), (b), (c) and (d) show variation of force with time. JEE Main 2023 (01 Feb Shift 2) JEE Main Previous Year Paper JEE Main 2023 (01 Feb Shift 2) JEE Main Previous Year Paper The impulse is highest in figure. (1) Fig (c) (2) Fig (b) (3) Fig (a) (4) Fig (d)

Q6. A nucleus disintegrates into two nuclear parts, in such a way that ratio of their nuclear sizes is 1 : 21/3 . Their respective speed have a ratio of n : 1 . The value of n is_________

Q6. A uniform solid cylinder with radius R and length L has moment of inertia I1 , about the axis of cylinder. A concentric solid cylinder of radius R′ = R2 and length L′ = L2 is carved out of the original cylinder. If I2 is the moment of inertia of the carved out portion of the cylinder then I1 = __________. I2 (Both I1 and I2 are about the axis of the cylinder)

Q6. If the gravitational field in the space is given as - 𝑟2. Taking the reference point to be at 𝑟= 2 cm with gravitational potential 𝑉= 10 J kg-1. Find the gravitational potentials at 𝑟= 3 cm in SI unit (Given, that 𝐾= 6 J cm kg-1) (1) 9 (2) 11 (3) 12 (4) 10