Practice Questions

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 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. 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. 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

Q6. Young’s moduli of the material of wires A and B are in the ratio of 1 : 4, while its area of cross sections are in the ratio of 1 : 3. If the same amount of load is applied to both the wires, the amount of elongation produced in the wires A and B will be in the ratio of [Assume length of wires A and B are same] (1) 12 : 1 (2) 1 : 36 (3) 36 : 1 (4) 1 : 12

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 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. 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 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. The momentum of a body is increased by 50% . The percentage increase in the kinetic energy of the body is_ _______%.

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

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. 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. 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_________

Q7. A solid sphere of mass 2 kg is making pure rolling on a horizontal surface with kinetic energy 2240 J. The velocity of centre of mass of the sphere will be ______ m s−1 .

Q7. The orbital angular momentum of a satellite is L, when it is revolving in a circular orbit at height h from earth surface. If the distance of satellite from the earth centre is increased by eight times to its initial value, then the new angular momentum will be (1) 8 L (2) 9 L (3) 4 L (4) 3 L

Q7. On a temperature scale '𝑋', the boiling point of water is 65°X and the freezing point is -15°X. Assuming that the 𝑋 scale is linear. The equivalent temperature corresponding to -95°X on the Fahrenheit scale would be (1) -112°F (2) -48°F (3) -148°F (4) -63°F

Q7. A machine gun of mass 10 kg fires 20 g bullets at the rate of 180 bullets per minute with a speed of 100 m s–1 each. The recoil velocity of the gun is : (1) 0. 02 m s−1 (2) 2. 5 m s−1 (3) 1. 5 m s−1 (4) 0. 6 m s−1

Q7. Choose the correct relationship between Poisson ratio 𝜎, bulk modulus ( 𝐾) and modulus of rigidity 𝜂 of a given solid object: (1) 𝜎= 3𝐾- 2𝜂 (2) 𝜎= 6𝐾+ 2𝜂 6𝐾+ 2𝜂 3𝐾- 2𝜂 3𝐾+ 2𝜂 6𝐾- 2𝜂 (3) 𝜎= (4) 𝜎= 6𝐾+ 2𝜂 3𝐾- 2𝜂

Q7. A mercury drop of radius 10 – 3 m is broken into 125 equal size droplets. Surface tension of mercury is 0 . 45 N m – 1 . The gain in surface energy is: (1) 2 . 26 × 10 – 5 J (2) 28 × 10 – 5 J (3) 17 . 5 × 10 – 5 J (4) 5 × 10 – 5 J JEE Main 2023 (01 Feb Shift 1) JEE Main Previous Year Paper

Q7. Given below are two statements: Statement I: Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface. JEE Main 2023 (24 Jan Shift 2) JEE Main Previous Year Paper Statement II: Acceleration due to earth's gravity is same at a height ' h' and depth ' d' from earth's surface, if h = d. In the light of above statements, choose the most appropriate answer form the options given below (1) Statement I is incorrect but statement II is correct (2) Both Statement I and Statement II are incorrect (3) Statement I is correct but statement II is incorrect (4) Both Statement I and II are correct

Q7. If a solid sphere of mass 5 kg and a disc of mass 4 kg have the same radius, then the ratio of moment of inertia of the disc about a tangent in its plane to the moment of inertia of the sphere about its tangent will be x . The 7 value of x is ______.

Q7. The weight of a body on the surface of the earth is 100 N . The gravitational force on it when taken at a height, from the surface of earth, equal to one-fourth the radius of the earth is: (1) 64 N (2) 25 N (3) 50 N (4) 100 N