Practice Questions

Q4. Consider a block kept on an inclined plane (inclined at 45° ) as shown in the figure. If the force required to just push it up the incline is 2 times the force required to just prevent it from sliding down, the coefficient of friction between the block and inclined plane (µ) is equal to : . (1) 0. 33 (2) 0. 60 (3) 0. 25 (4) 0. 50

Q4. The position vector of a particle related to time t is given by →r= (10tˆi + 15t2ˆj + 7ˆk)m . The direction of net force experienced by the particle is : (1) Positive x-axis (2) In x −y plane (3) Positive y-axis (4) Positive z-axis

Q4. A small particle of mass m moves in such a way that its potential energy U = 12 mω2r2 where ω is constant and r is the distance of the particle from origin. Assuming Bohr’s quantization of momentum and circular orbit, the radius of nth orbit will be proportional to (1) √n (2) n1 (3) n2 (4) n

Q4. Given below are two statements: Statement I : Rotation of the earth shows effect on the value of acceleration due to gravity ( 𝑔) . Statement II : The effect of rotation of the earth on the value of 𝑔 at the equator is minimum and that at the pole is maximum. In the light of the above statements, choose the correct answer from the options given below (1) Statement I is false but statement II is true (2) Both Statement I and Statement II are true (3) Both Statement I and Statement II are false (4) Statement I is true but statement II is false

Q4. Two bodies are projected from ground with same speeds 40 m s−1 at two different angles with respect to horizontal. The bodies were found to have same range. If one of the body was projected at an angle of 60° , with horizontal then sum of the maximum heights, attained by the two projectiles, is _____ m. (Given g = 10 m s−2 )

Q4. A body of mass 500 g moves along x-axis such that it's velocity varies with displacement x according to the relation v = 10√x m s−1 the force acting on the body is: (1) 125 N (2) 25 N (3) 166 N (4) 5 N

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. The radii of two planets 𝐴 and 𝐵 are 𝑅 and 4𝑅 and their densities are 𝜌 and respectively. The ratio of 3 acceleration due to gravity at their surfaces 𝑔𝐴: 𝑔𝐵 will be (1) 4: 3 (2) 1: 16 (3) 3: 16 (4) 3: 4 Q6. 1 kg of water at 100°C is converted into steam at 100°C by boiling at atmospheric pressure. The volume of water changes from 1 . 00 × 10-3 m3 as a liquid to 1 . 671 m3 as steam. The change in internal energy of the system during the process will be (Given latent heat of vaporisation = 2257 kJ / kg, Atmospheric pressure = 1 × 105 Pa (1) -2426 kJ (2) +2090 kJ (3) -2090 kJ (4) +2476 kJ JEE Main 2023 (11 Apr Shift 1) JEE Main Previous Year Paper

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

Q5. A nucleus disintegrates into two smaller parts, which have their velocities in the ratio 3 : 2 . The ratio of their 1 nuclear sizes will be ( x3 ) 3 . The value of ‘ x’ is:

Q5. A block of mass 5 kg starting from rest pulled up on a smooth incline plane making an angle of 30° with horizontal with an effective acceleration of 1 m s−2 . The power delivered by the puling force at t = 10 s from the start is _____ W. [Use g = 10 m s−2 ] (Calculate the nearest integer value)

Q5. To maintain a speed of 80 km h−1 by a bus of mass 500 kg on a plane rough road for 4 km distance, the work done by the engine of the bus will be _____ kJ. [The coefficient of friction between tyre of bus and road is 0. 04 ]

Q5. A body of mass 5 kg is moving with a momentum of 10 kg m s−1 . Now a force of 2 N acts on the body in the direction of its motion for 5 s. The increase in the Kinetic energy of the body is _____ J.

Q5. A particle of mass 100 g is projected at time t = 0 with a speed 20 m s–1 at an angle 45° to the horizontal as given in the figure. The magnitude of the angular momentum of the particle about the starting point at time t = 2 s is found to be √K kg m2 s−1 . The value of K is ______. (Take g = 10 m s−2 )

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 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. Two bodies are having kinetic energies in the ratio 16 : 9. If they have same linear momentum, the ratio of their masses respectively is: (1) 3 : 4 (2) 9 : 16 (3) 16 : 9 (4) 4 : 3

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. 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 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. 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. An object of mass m initially at rest on a smooth horizontal plane starts moving under the action of force F = 2 N . In the process of its linear motion, the angle θ (as shown in figure) between the direction of force and horizontal varies as θ = kx , where k is a constant and x is the distance covered by the object from its initial position. The expression of kinetic energy of the object will be E = nk sin θ . The value of n is ______.

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 weight of a body at the surface of earth is 18 N. The weight of the body at an altitude of 3200 km above the earth's surface is (given, radius of earth 𝑅𝑒= 6400 km) (1) 9 . 8 N (2) 4 . 9 N (3) 19 . 6 N (4) 8 N

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