Practice Questions

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. 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. 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

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. 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. The moment of inertia of a semicircular ring about an axis, passing through the center and perpendicular to the plane of ring, is 1 MR2 , where R is the radius and M is the mass of the semicircular ring. The value of x will x be _______ .

Q7. Two satellites A and B move round the earth in the same orbit. The mass of A is twice the mass of B. The quantity which is same for the two satellites will be (1) Speed (2) Kinetic energy (3) Total energy (4) Potential energy

Q7. A solid sphere is rolling on a horizontal plane without slipping. If the ratio of angular momentum about axis of rotation of the sphere to the total energy of moving sphere is π : 22 then, the value of its angular speed will be _________rad s−1. JEE Main 2023 (13 Apr Shift 1) JEE Main Previous Year Paper

Q7. A circular plate is rotating in horizontal plane, about an axis passing through its centre and perpendicular to the plate, with an angular velocity ω. A person sits at the centre having two dumbbells in his hands. When he stretched out his hands, the moment of inertia of the system becomes triple. If E be the initial Kinetic energy of the system, then final Kinetic energy will be E . The value of x is x

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. 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. 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. Force acts for 20 s on a body of mass 20 kg , starting from rest, after which the force ceases and then body describes 50 m in the next 10 s . The value of force will be : JEE Main 2023 (29 Jan Shift 2) JEE Main Previous Year Paper (1) 40 N (2) 5 N (3) 20 N (4) 10 N

Q7. Moment of inertia of a disc of mass M and radius ' R' about any of its diameter is MR2 . The moment of inertia 4 of this disc about an axis normal to the disc and passing through a point on its edge will be, x MR2 . The value 2 of x is ______.

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. 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

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 ______.

Q8. Identify the correct statements from the following: (A) Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket is negative (B) Work done by gravitational force in lifting a bucket out of a well by a rope tied to the bucket is negative (C) Work done by friction on a body sliding down an inclined plane is positive (D) Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity is zero (E) Work done by the air resistance on an oscillating pendulum is negative Choose the correct answer from the options given below: (1) B and E only (2) A and C only (3) B, D and E only (4) B and D only

Q8. A small ball of mass 𝑀 and density 𝜌 is dropped in a viscous liquid of density 𝜌0. After some time, the ball falls with a constant velocity. What is the viscous force on the ball? 𝜌0 𝜌 (1) 𝐹= 𝑀𝑔1 + (2) 𝐹= 𝑀𝑔1 + 𝜌 𝜌0 𝜌0 (3) 𝐹= 𝑀𝑔1 - (4) 𝐹= 𝑀𝑔1 ± 𝜌𝜌0 𝜌

Q8. A sample of gas at temperature 𝑇 is adiabatically expanded to double its volume. The work done by the gas in 3 the process is given, (given 𝛾= 2) : - 2 (1) 𝑊= 𝑇𝑅√2 - 2 (2) 𝑊= 𝑅√2𝑇 𝑅 (3) 𝑊= 𝑇2 - √2 (4) 𝑊= 𝑅𝑇2 - √2

Q8. Given below are two statements: Statement I: If E be the total energy of a satellite moving around the earth, then its potential energy will be E . 2 Statement II: The kinetic energy of a satellite revolving in an orbit is equal to the half the magnitude of total energy E . In the light of the above statements, choose the most appropriate answer from the options given below. (1) Statement I is correct but Statement II is incorrect (2) Statement I is incorrect but Statement II is correct (3) Both Statement I and Statement II are correct (4) Both Statement I and Statement II are incorrect

Q8. Two particles of equal mass m move in a circle of radius r under the action of their mutual gravitational attraction. The speed of each particle will be : (1) √Gm2r (2) √4Gmr (3) √Gmr (4) √Gm4r