Practice Questions

Q5. A body is released from a height equal to the radius (R) of the earth. The velocity of the body when it strikes the surface of the earth will be: (Given g = acceleration due to gravity on the earth.) (1) √2gR (2) √gR (3) √4gR (4) √gR2

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

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. 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 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. 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. 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. 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. 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. 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. 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

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. 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. 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. 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. 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 wire of length L and radius r is clamped rigidly at one end. When the other end of the wire is pulled by a force f , its length increases by l. Another wire of same material of length 2L and radius 2r is pulled by a force 2f . Then the increase in its length will be: (1) 4l (2) 2l (3) 2l (4) l

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. 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

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. The height of liquid column raised in a capillary tube of certain radius when dipped in liquid 𝐴 vertically is, 5 cm. If the tube is dipped in a similar manner in another liquid 𝐵 of surface tension and density double the JEE Main 2023 (30 Jan Shift 1) JEE Main Previous Year Paper values of liquid 𝐴, the height of liquid column raised in liquid B would be ______ m. (1) 0 . 20 (2) 0 . 5 (3) 0 . 05 (4) 0 . 10

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. The escape velocities of two planets A and B are in the ratio 1 : 2 . If the ratio of their radii respectively is 1 : 3 , then the ratio of acceleration due to gravity of planet A to the acceleration of gravity of planet B will be: (1) 4 (2) 3 3 2 (3) 2 (4) 3 3 4

Q8. The acceleration due to gravity at height h above the earth if h ≪R (Radius of earth) is given by − 2R2 (1) g′ = g(1 h2 ) (2) g′ = g(1 − 2Rh ) (3) g′ = g(1 −2hR ) (4) g′ = g(1 −2h2R2 )

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