Practice Questions

Q5. A √34 m long ladder weighing 10 kg leans on a frictionless wall. Its feet rest on the floor 3 m away from the wall as shown in the figure. If Ff and Fw are the reaction forces of the floor and the wall, then ratio of Fw will Ff be : (Use g = 10 m s−2 .) (1) 6 (2) 3 √110 √113 (3) 3 (4) 2 √109 √109

Q5. If momentum of a body is increased by 20%, then its kinetic energy increases by : (1) 36% (2) 40% (3) 44% (4) 48%

Q5. A body is projected vertically upwards from the surface of earth with a velocity equal to one third of escape velocity. The maximum height attained by the body will be (Take radius of earth = 6400 km and 𝑔= 10 ms-2) (1) 800 km (2) 1600 km (3) 2133 km (4) 4800 km

Q5. Two satellites A and B having masses in the ratio 4 : 3 are revolving in circular orbits of radii 3r and 4r respectively around the earth. The ratio of total mechanical energy of A to B is (1) 9 : 16 (2) 16 : 9 (3) 1 : 1 (4) 4 : 3

Q5. If the radius of earth shrinks by 2% while its mass remains same. The acceleration due to gravity on the earth's surface will approximately (1) decrease by 2% (2) decrease by 4% (3) increase by 2% (4) increase by 4%

Q5. Two planets A and B of equal mass are having their period of revolutions TA and TB such that TA = 2TB . These planets are revolving in the circular orbits of radii rA and rB respectively. Which out of the following would be the correct relationship of their orbits? (1) 2r2A = r3B (2) r3A = 2r3B (3) r3A = 4r3B (4) T A2 −T B2 = GMπ2 (r3B −4r3A)

Q6. Three identical particle 𝐴, 𝐵 and 𝐶 of mass 100 kg each are placed in a straight line with 𝐴𝐵= 𝐵𝐶= 13 m. The gravitational force on a fourth particle 𝑃 of the same mass is 𝐹, when placed at a distance 13 m from the particle 𝐵 on the perpendicular bisector of the line 𝐴𝐶. The value of 𝐹 will be approximately (1) 21G (2) 100G (3) 59G (4) 42G

Q6. If p is the density and η is coefficient of viscosity of fluid which flows with a speed v in the pipe of diameter d, the correct formula for Reynolds number Re is (1) Re = πdρv (2) Re = ηdρv (3) Re = ρvdη (4) Re = ρνdη

Q6. The force required to stretch a wire of cross-section 1 cm2 to double its length will be : (Given Yong's modulus of the wire = 2 × 1011 N m-2) (1) 1 × 107 N (2) 1 . 5 × 107 N (3) 2 × 107 N (4) 2 . 5 × 107 N

Q6. The time period of a satellite revolving around earth in a given orbit is 7 hours. If the radius of orbit is increased to three times its previous value, then approximate new time period of the satellite will be (1) 36 hours (2) 40 hours (3) 30 hours (4) 25 hours JEE Main 2022 (29 Jun Shift 2) JEE Main Previous Year Paper

Q6. What percentage of kinetic energy of a moving particle is transferred to a stationary particle when it strikes the stationary particle of 5 times its mass? (Assume the collision to be head-on elastic collision) (1) 50. 0% (2) 66. 6% (3) 55. 6% (4) 33. 3%

Q6. Two cylindrical vessels of equal cross-sectional area 16 cm2 contain water upto heights 100 cm and 150 cm respectively. The vessels are interconnected so that the water levels in them become equal. The work done by the force of gravity during the process, is [Take density of water = 103 kg m−3 and g = 10 ms−2 ] (1) 0. 25 J (2) 1 J (3) 8 J (4) 12 J JEE Main 2022 (27 Jul Shift 1) JEE Main Previous Year Paper

Q6. A body of mass m is projected with velocity λve in vertically upward direction from the surface of the earth into space. It is given that ve is escape velocity and λ < 1 . If air resistance is considered to the negligible, then the maximum height from the centre of earth, to which the body can go, will be ( R : radius of earth) (1) R (2) R 1+λ2 1−λ2 (3) R (4) λ2R 1−λ 1−λ2

Q6. A copper block of mass 5 . 0 kg is heated to a temperature of 500°C and is placed on a large ice block. What is the maximum amount of ice that can melt? [Specific heat of copper : 0 . 39Jg-1∘C-1 and latent heat of fusion of water : 335 Jg-1] (1) 1 . 5 kg (2) 5 . 8 kg (3) 2 . 9 kg (4) 3 . 8 kg 𝐶𝑃

Q6. A water drop of radius 1 cm is broken into 729 equal droplets. If surface tension of water is 75 dyne cm−1 , then the gain in surface energy upto first decimal place will be [Given π = 3. 14 ] JEE Main 2022 (26 Jul Shift 1) JEE Main Previous Year Paper (1) 8. 5 × 10−4 J (2) 8. 2 × 10−4 J (3) 7. 5 × 10−4 J (4) 5. 3 × 10−4 J Q7. 7 mole of certain monoatomic ideal gas undergoes a temperature increase of 40 K at constant pressure. The increase in the internal energy of the gas in this process is (Given R = 8. 3 J K−1 mol−1 ) (1) 5810 J (2) 3486 J (3) 11620 J (4) 6972 J

Q6. Two objects of equal masses placed at certain distance from each other attracts each other with a force of F . If one-third mass of one object is transferred to the other object, then the new force will be JEE Main 2022 (28 Jun Shift 2) JEE Main Previous Year Paper (1) 2 F (2) 16 F 9 9 (3) 8 F (4) F 9

Q6. Two bodies of mass 1 kg and 3 kg have position vectors ˆi + 2ˆj + ˆk and −3ˆi −2ˆj + ˆk respectively. The magnitude of position vector of centre of mass of this system will be similar to the magnitude of vector : (1) ˆi −2ˆj + ˆk (2) −3ˆi −2ˆj + ˆk (3) −2ˆi + 2ˆk (4) −2ˆi −ˆj + 2ˆk

Q6. A body of mass M at rest explodes into three pieces, in the ratio of masses 1 : 1 : 2 . Two smaller pieces fly off perpendicular to each other with velocities of 30 m s−1 and 40 m s−1 respectively. The velocity of the third piece will be (1) 35 m s−1 (2) 50 m s−1 (3) 25 m s−1 (4) 15 m s−1

Q6. A water drop of diameter 2 cm is broken into 64 equal droplets. The surface tension of water is 0. 075 N m−1 . In this process the gain in surface energy will be (1) 2. 8 × 10−4 J (2) 1. 5 × 10−3 J (3) 1. 9 × 10−4 J (4) 9. 4 × 10−5 J

Q6. A pressure-pump has a horizontal tube of cross-sectional area 10 cm2 for the outflow of water at a speed of 20 m s−1 . The force exerted on the vertical wall just in front of the tube which stops water horizontally flowing out of the tube, is: [given : density of water = 1000 kg m−3 ] (1) 300 N (2) 500 N (3) 250 N (4) 400 N

Q6. A stone tide to a string of length L is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of change in its velocity, as it reaches a position where the string is horizontal, is √x(u2 −gL). The value of x is (1) 2 (2) 3 (3) 4 (4) 1

Q6. The torque of a force 5 ^𝑖+ 3 ^𝑗- 7 ^𝑘 about the origin is 𝜏. If the force acts on a particle whose position vector is 2 ^𝑖+ 2 ^𝑗+ ^𝑘, then the value of 𝜏 will be (1) 11 ^𝑖+ 19 ^𝑗- 4 ^𝑘 (2) -11 ^𝑖+ 9 ^𝑗- 16 ^𝑘 (3) -17 ^𝑖+ 19 ^𝑗- 4 ^𝑘 (4) 17 ^𝑖+ 9 ^𝑗+ 16 ^𝑘

Q6. The terminal velocity 𝑣𝑡 of the spherical rain drop depends on the radius 𝑟 of the spherical rain drop as (1) 𝑟 (2) 𝑟2 1 1 (3) (4) 𝑟 𝑟2

Q6. The distance between Sun and Earth is R. The duration of year if the distance between Sun and Earth becomes 3R will be : (1) √3 yr (2) 3√3 yr (3) 3 yr (4) 9 yr

Q6. The approximate height from the surface of earth at which the weight of the body becomes 1 of its weight on 3 the surface of earth is : [Radius of earth R = 6400 km and √3 = 1. 732 ] (1) 3840 km (2) 4685 km (3) 2133 km (4) 4267 km