Practice Questions

Q4. A body of mass 4 kg experiences two forces →𝐹1 = 5 ^𝑖+ 8 ^𝑗+ 7 ^𝑘 and →𝐹2 = 3 ^𝑖- 4 ^𝑗- 3 ^𝑘. The acceleration acting on the body is: (1) -2 ^𝑖- ^𝑗- ^𝑘 (2) 4 ^𝑖+ 2 ^𝑗+ 2 ^𝑘 (3) 2 ^𝑖+ ^𝑗+ ^𝑘 (4) 2 ^𝑖+ 3 ^𝑗+ 3 ^𝑘

Q4. A heavy box of mass 50 kg is moving on a horizontal surface. If co-efficient of kinetic friction between the box and horizontal surface is 0.3 then force of kinetic friction is : (1) 1.47 N (2) 147 N (3) 14.7 N (4) 1470 N

Q4. A particle is placed at the point A of a frictionless track ABC as shown in figure. It is gently pushed towards right. The speed of the particle when it reaches the point B is: (Take g = 10 m s−2). (1) 20 m s−1 (2) √10 m s−1 (3) 2√10 m s−1 (4) 10 m s−1

Q4. A block of mass 100 kg slides over a distance of 10 m on a horizontal surface. If the co-efficient of friction between the surfaces is 0. 4 , then the work done against friction (in J) is: (1) 4200 (2) 3900 (3) 4000 (4) 4500

Q4. A thin circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with angular velocity ω. If another disc of same dimensions but of mass M/2 is placed gently on the first disc co-axially, then the new angular velocity of the system is : (1) 3 ω (2) 5 ω 2 4 (3) 2 ω (4) 4 ω 3 5

Q5. Three bodies A, B and C have equal kinetic energies and their masses are 400 g. 1.2 kg and 1.6 kg respectively. The ratio of their linear momenta is : (1) √2; √3; 1 (2) 1 : √3 : 2 (3) 1 : √3 : √2 (4) √3 : √2 : 1

Q5. A body of mass 1000 kg is moving horizontally with a velocity 6 m s−1 . If 200 kg extra mass is added, the final velocity (in m s−1 ) is: (1) 6 (2) 2 (3) 3 (4) 5

Q5. A bullet of mass 50 g is fired with a speed 100 m/s on a plywood and emerges with 40 m/s. The percentage loss of kinetic energy is : (1) 84% (2) 16% (3) 32% (4) 44%

Q5. The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is: (1) 1 : 9 (2) 1 : 3 (3) 1 : 27 (4) 1 : 81

Q5. A body of mass 50 kg is lifted to a height of 20 m from the ground in the two different ways as shown in the figures. The ratio of work done against the gravity in both the respective cases, will be : (1) 1 : 2 (2) √3 : 2 (3) 2 : 1 (4) 1 : 1

Q6. Escape velocity of a body from earth is 11 . 2 km s-1. If the radius of a planet be one-third the radius of earth and mass be one-sixth that of earth, the escape velocity from the plate is: (1) 11 . 2 km s-1 (2) 8 . 4 km s-1 (3) 4 . 2 km s-1 (4) 7 . 9 km s-1

Q6. Two satellite A and B go round a planet in circular orbits having radii 4R and R respectively. If the speed of A is 3v, the speed of B will be : (1) 3v (2) 6v (3) 4 v (4) 12v 3

Q6. Assuming the earth to be a sphere of uniform mass density, a body weighed 300 N on the surface of earth. How much it would weigh at R/4 depth under surface of earth ? (1) 75 N (2) 300 N (3) 375 N (4) 225 N

Q6. A coin is placed on a disc. The coefficient of friction between the coin and the disc is 𝜇. If the distance of the coin from the center of the disc is 𝑟, the maximum angular velocity which can be given to the disc, so that the coin does not slip away, is : JEE Main 2024 (31 Jan Shift 1) JEE Main Previous Year Paper 𝜇𝑔 𝑟 (1) (2) 𝑟 √ 𝜇𝑔 𝜇𝑔 𝜇 (3) (4) √ 𝑟 √𝑟𝑔

Q6. The acceleration due to gravity on the surface of earth is g. If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be : (1) g (2) 2g 4 (3) g (4) 4g 2

Q6. Four particles A, B, C, D of mass m2 , m, 2m, 4m, have same momentum, respectively. The particle with maximum kinetic energy is : (1) B (2) A (3) D (4) C

Q6. A planet takes 200 days to complete one revolution around the Sun. If the distance of the planet from Sun is reduced to one fourth of the original distance, how many days will it take to complete one revolution? (1) 25 (2) 50 (3) 100 (4) 20 JEE Main 2024 (29 Jan Shift 2) JEE Main Previous Year Paper

Q6. If a rubber ball falls from a height h and rebounds upto the height of h/2. The percentage loss of total energy of the initial system as well as velocity ball before it strikes the ground, respectively, are : (1) 50%, √2gh (2) 50%, √gh (3) 40%, √2gh (4) 50%, √gh2 JEE Main 2024 (04 Apr Shift 1) JEE Main Previous Year Paper

Q7. Young's modules of material of a wire of length L and cross-sectional area A is Y . If the length of the wire is doubled and cross-sectional area is halved then Young's modules will be: (1) Y (2) 4Y 4 (3) Y (4) 2Y

Q8. A gas mixture consists of 8 moles of argon and 6 moles of oxygen at temperature 𝑇. Neglecting all vibrational modes, the total internal energy of the system is (1) 29 𝑅𝑇 (2) 20 𝑅𝑇 (3) 27 𝑅𝑇 (4) 21 𝑅𝑇

Q8. The temperature of a gas is −78∘C and the average translational kinetic energy of its molecules is K. The temperature at which the average translational kinetic energy of the molecules of the same gas becomes 2 K is : (1) 127∘C (2) 117∘C (3) −39∘C (4) −78∘C

Q9. The translational degrees of freedom (ft) and rotational degrees of freedom (fr) of CH4 molecule are: (1) ft = 2 and fr = 2 (2) ft = 3 and fr = 3 (3) ft = 3 and fr = 2 (4) ft = 2 and fr = 3

Q9. The temperature of a gas having 2. 0 × 1025 molecules per cubic meter at 1. 38 atm (Given, k = 1. 38 × 10−23J K−1) is : (1) 500 K (2) 200 K (3) 100 K (4) 300 K

Q9. A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the sample, is: (1) 1 (2) 2√2 32 1 (3) 1 (4) 1 2√2 4

Q9. The total kinetic energy of 1 mole of oxygen at 27°C is : [Use universal gas constant (R) = 8 . 31 J mol-1 K-1 ] (1) 6845 . 5 J (2) 5942 . 0 J (3) 6232 . 5 J (4) 5670 . 5 J