Practice Questions

Q2. Match List I with List II List I List II A Angular momentum I [ML2 T−2] B Torque II [ML−2 T−2] C Stress III [ML2 T−1] D Pressure gradient IV [ML−1 T−2] Choose the correct answer from the options given below : (1) A-I, B-IV, C-III, D-II (2) A-III, B-I, C-IV, D-II (3) A-II, B-III, C-IV, D-I (4) A-IV, B-II, C-I, D-III

Q2. Given below are two statements: Statement I: Area under velocity-time graph gives the distance travelled by the body in a given time. Statement II: Area under acceleration-time graph is equal to the change in velocity in the given time. In the light of given statements, choose the correct answer from the options given below. (1) Both Statement I and Statement II are true (2) Both Statement I and Statement II are false (3) Statement I is correct but Statement II is false (4) Statement I is incorrect but Statement II is true x and y are measured in

Q2. Match List I with List II List-I List-II A Spring constant I [T –1] B Angular speed II [MT –2] C Angular momentum III [ML2] D Moment of Inertia IV [ML2T –1] Choose the correct answer from the options given below: (1) A-I, B-III, C-II, D-IV (2) A-IV, B-I, C-III, D-II (3) A-II, B-I, C-IV, D-III (4) A-II, B-III, C-I, D-IV

Q2. A particle is moving with constant speed in a circular path. When the particle turns by an angle 90°, the ratio of instantaneous velocity to its average velocity is 𝜋: 𝑥√2 . The value of 𝑥 will be (1) 2 (2) 5 (3) 1 (4) 7

Q2. The distance travelled by a particle is related to time t as x = 4t2 . The velocity of the particle at t = 5 s is (1) 40 m s–1 (2) 25 m s–1 (3) 20 m s–1 (4) 8 m s–1

Q2. The initial speed of a projectile fired from ground is 𝑢. At the highest point during its motion, the speed of √3 projectile is 𝑢. The time of flight of the projectile is: 2 (1) 𝑢 (2) 𝑢 2𝑔 𝑔 2𝑢 √3𝑢 (3) (4) 𝑔 𝑔

Q2. Two forces having magnitude A and A2 are perpendicular to each other. The magnitude of their resultant is: (1) √5A (2) √5A 4 2 (3) 5A (4) √5A2 2 2

Q2. For a train engine moving with speed of 20 ms–1 , the driver must apply brakes at a distance of 500 m before the station for the train to come to rest at the station. If the brakes were applied at half of this distance, the train engine would cross the station with speed √x ms−1 . The value of x is ______. (Assuming same retardation is produced by brakes)

Q2. The position-time graphs for two students 𝐴 and 𝐵 returning from the school to their homes are shown in figure. (A) 𝐴 lives closer to the school (B) 𝐵 lives closer to the school (C) 𝐴 takes lesser time to reach home (D) 𝐴 travels faster than 𝐵 (E) 𝐵 travels faster than 𝐴 Choose the correct answer from the options given below (1) A, C and D only (2) A, C and E only (3) B and E only (4) A and E only

Q3. The position of a particle related to time is given by x = (5t2 −4t + 5) m. The magnitude of velocity of the particle at t = 2 s will be : (1) 06 m s−1 (2) 14 m s−1 (3) 10 m s−1 (4) 16 m s−1

Q3. A stone is projected at angle 30° to the horizontal. The ratio of kinetic energy of the stone at point of projection to its kinetic energy at the highest point of flight will be : (1) 1 : 2 (2) 1 : 4 (3) 4 : 1 (4) 4 : 3

Q3. A stone of mass 1 kg is tied to end of a massless string of length 1 m. If the breaking tension of the string is 400 N , then maximum linear velocity, the stone can have without breaking the string, while rotating in horizontal plane, is: (1) 20 m s−1 (2) 40 m s−1 (3) 400 m s−1 (4) 10 m s−1

Q3. A child of mass 5 kg is going round a merry-go-round that makes 1 rotation in 3. 14 s. The radius of the merry- go-round is 2 m. The centrifugal force on the child will be (1) 80 N (2) 40 N (3) 100 N (4) 50 N

Q3. A car travels a distance of x with speed v1 and then same distance x with speed v2 in the same direction. The average speed of the car is: (1) v1v2 (2) v1+v2 2(v1+v2) 2 (3) 2x (4) 2v1v2 v1+v2 v1+v2

Q3. As per given figure, a weightless pulley 𝑃 is attached on a double inclined frictionless surface. The tension in the string (massless) will be (if 𝑔= 10 m s-2) (1) 4√3 + 1 N (2) 4√3 + 1 N (3) 4√3 - 1 N (4) 4√3 - 1 N

Q3. The velocity-time graph of a body moving in a straight line is shown in figure. The ratio of displacement and distance travelled by the body in time 0 to 10 s is (1) 1 : 1 (2) 1 : 2 (3) 1 : 3 (4) 1 : 4

Q3. A coin placed on a rotating table just slips when it is placed at a distance of 1 cm from the centre. If the angular velocity of the table is halved, it will just slip when placed at a distance of _____ from the centre: (1) 8 cm (2) 4 cm (3) 1 cm (4) 2 cm

Q3. Given below are two statements: one is labelled as Assertion 𝐴 and the other is labelled as Reason 𝑅. Assertion A: When a body is projected at an angle 45°, its range is maximum. Reason R: For maximum range, the value of sin 2𝜃 should be equal to one. In the light of the above statements, choose the correct answer from the options given below: (1) 𝐴 is false but 𝑅 is true (2) 𝐴 is true but 𝑅 is false (3) Both 𝐴 and 𝑅 are correct and 𝑅 is the correct (4) Both 𝐴 and 𝑅 are correct but 𝑅 is NOT the correct explanation of 𝐴 explanation of 𝐴

Q3. As shown in figure, a 70 kg garden roller is pushed with a force of →𝐹= 200 N at an angle of 30° with horizontal. The normal reaction on the roller is (Given 𝑔= 10 m s-2) (1) 800√2 N (2) 600 N (3) 800 N (4) 200√3 N Q4. 100 balls each of mass 𝑚 moving with speed 𝑣 simultaneously strike a wall normally and reflected back with same speed, in time 𝑡 s. The total force exerted by the balls on the wall is 100𝑚𝑣 200𝑚𝑣 (1) (2) 𝑡 𝑡 (3) 200 𝑚𝑣𝑡 (4) 𝑚𝑣 100𝑡

Q3. A projectile is projected at 30° from horizontal with initial velocity 40 m s−1 . The velocity of the projectile at t = 2 s from the start will be: (1) 40√3 m s−1 (2) Zero (3) 20 m s−1 (4) 20√3 m s−1

Q3. The ratio of powers of two motors is 3√x , that are capable of raising 300 kg water in 5 minutes and 50 kg √x+1 water in 2 minutes respectively from a well of 100 m deep. The value of x will be (1) 16 (2) 2 (3) 2. 4 (4) 4

Q3. The figure represents the momentum time ( 𝑝- 𝑡) curve for a particle moving along an axis under the influence of the force. Identify the regions on the graph where the magnitude of the force is maximum and minimum respectively ? If 𝑡3 - 𝑡2 < 𝑡1 JEE Main 2023 (30 Jan Shift 1) JEE Main Previous Year Paper (1) c and a (2) b and c (3) c and b (4) a and b

Q3. As shown in the figure a block of mass 10 kg lying on a horizontal surface is pulled by a force F acting at an angle 30° , with horizontal. For μs = 0. 25 , the block will just start to move for the value of F : [Given g = 10 m ⋅s–2 ] (1) 33. 3 N (2) 25. 2 N (3) 20 N (4) 35. 7 N

Q3. Two objects are projected with same velocity u however at different angles α and β with the horizontal. If α + β = 90° , the ratio of horizontal range of the first object to the 2nd object will be : (1) 4 : 1 (2) 2 : 1 (3) 1 : 2 (4) 1 : 1

Q3. An object is allowed to fall from a height R above the earth, where R is the radius of earth. Its velocity when it strikes the earth’s surface, ignoring air resistance, will be : (1) 2√gR (2) √gR (3) √gR2 (4) √2gR