Practice Questions

Q2. The maximum vertical height to which a man can throw a ball is 136 m. The maximum horizontal distance upto which he can throw the same ball is (1) 192 m (2) 136 m (3) 272 m (4) 68 m

Q2. A tennis ball is dropped on to the floor from a height of 9. 8 m. It rebounds to a height 5. 0 m. Ball comes in contact with the floor for 0. 2 s . The average acceleration during contact is ______ m s−2 . [Given g = 10 m s−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 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. The speed of a wave produced in water is given by ν = λagbρc . Where λ, g and ρ are wavelength of wave, acceleration due to gravity and density of water respectively. The values of a, b and c respectively, are (1) 1, −1, 0 (2) 12 , 0, 12 (3) 1, 1, 0 (4) 21 , 12 , 0

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

Q3. The trajectory of projectile, projected from the ground is given by y = x −x220 . Where meter. The maximum height attained by the projectile will be. (1) 200 m (2) 10 m (3) 5 m (4) 10√2 m

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 ball is thrown vertically upward with an initial velocity of 150 m s−1 . The ratio of velocity after 3 s and 5 s is x+1 . The value of x is _____. {take, g = 10 m s−2 } x (1) 10 (2) −5 (3) 6 (4) 5

Q3. A child stands on the edge of the cliff 10 m above the ground and throws a stone horizontally with an initial speed of 5 m s – 1 . Neglecting the air resistance, the speed with which the stone hits the ground will be _____ m s – 1 (given, 𝑔 = 10 m s – 2 ). (1) 20 (2) 15 (3) 30 (4) 25

Q3. The range of the projectile projected at an angle of 15∘ with horizontal is 50 m. If the projectile is projected with same velocity at an angle of 45∘ with horizontal, then its range will be (1) 100 m (2) 100√2 m (3) 50√2 m (4) 50 m

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. 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

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 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. 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. 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. 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. A passenger sitting in a train A moving at 90 km h-1 observes another train B moving in the opposite direction for 8 s. If the velocity of the train B is 54 km h-1, then length of train B is: (1) 120 m (2) 320 m (3) 80 m (4) 200 m

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 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 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. An object moves at a constant speed along a circular path in a horizontal plane with centre at the origin. When the object is at x = +2 m, its velocity is −4ˆj m s−1 . The object’s velocity (v) and acceleration (a) at x = –2 m will be (1) v = 4ˆi m s−1, a = 8ˆj m s−2 (2) v = 4ˆj m s−1, a = 8ˆi m s−2 (3) v = −4ˆj m s−1, a = 8ˆi m s−2 (4) v = −4ˆi m s−1, a = −8ˆj m s−2

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. 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