Practice Questions

Q5. Two planets A and B of radii 𝑅 and 1 . 5 𝑅 have densities 𝜌 and 𝜌 respectively. The ratio of acceleration due to 2 gravity at the surface of B to A is: (1) 2 : 3 (2) 2 : 1 (3) 3 : 4 (4) 4 : 3

Q5. A block of mass m slides down the plane inclined at angle 30° with an acceleration 4g . The value of coefficient of kinetic friction will be : (1) 2√3+1 (2) 1 2 2√3 (3) √3 (4) 2√3−1 2 2

Q5. A small block of mass 100 g is tied to a spring of spring constant 7 . 5 N m-1 and length 20 cm . The other end of spring is fixed at a particular point 𝐴. If the block moves in a circular path on a smooth horizontal surface with constant angular velocity 5 rad s-1about point 𝐴, then tension in the spring is (1) 0 . 75 N (2) 0 . 25 N (3) 0 . 50 N (4) 1 . 5 N

Q5. A block of √3 kg is attached to a string whose other end is attached to the wall. An unknown force F is applied so that the string makes an angle of 30° with the wall. The tension T is : (Given g = 10 m s–2 ) (1) 20 N (2) 25 N (3) 10 N (4) 15 N

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 body of mass 10 kg is moving with an initial speed of 20 m s−1 . The body stops after 5 s due to friction between body and the floor. The value of the coefficient of friction is: (Take acceleration due to gravity g = 10 m s−2 ) (1) 0. 2 (2) 0. 3 (3) 0. 5 (4) 0. 4

Q5. At a certain depth 𝑑 below surface of earth, value of acceleration due to gravity becomes four times that of its value at a height 3𝑅 above earth surface. Where 𝑅 is Radius of earth (Take 𝑅 = 6400 km). The depth 𝑑 is equal to (1) 5260 km (2) 640 km (3) 2560 km (4) 4800 km

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. If earth has a mass nine times and radius twice to the of a planet 𝑃. Then 3 √𝑥𝑚𝑠-1 will be the minimum velocity required by a rocket to pull out of gravitational force of 𝑃, where ve is escape velocity on earth. The value of 𝑥 is (1) 2 (2) 3 (3) 18 (4) 1

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

Q5. Two satellites of masses m and 3 m revolve around the earth in circular orbits of radii r & 3r respectively. The ratio of orbital speeds of the satellites respectively is (1) √3: 1 (2) 3: 1 (3) 9: 1 (4) 1: 1

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. 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. 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. 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. 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 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

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 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. 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. 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. 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. 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 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