Practice Questions

Q2. The equation of a circle is given by x2 + y2 = a2 , where a is the radius. If the equation is modified to change the origin other than (0, 0), then find out the correct dimensions of A and B in a new equation : (x −At)2 + (y − Bt ) 2 = a2 The dimensions of t is given as [T−1] (1) A = [L–1T], B = [LT–1] (2) A = [LT], B = [L–1T –1] (3) A = [L–1T –1 ], B = [LT–1] (4) A = [L–1T –1], B = [LT]

Q2. The distance travelled by an object in time 𝑡 is given by 𝑠= 2 . 5𝑡2 . The instantaneous speed of the object at 𝑡= 5 s will be : (1) 25 m s – 1 (2) 5 m s – 1 (3) 62 . 5 m s – 1 (4) 12 . 5 m s – 1

Q2. Match List I with List II List - I List - II A Surface tension I. kg m−1 s−1 B Pressure II. kg m s−1 C Viscosity III. kg m−1 s−2 D Impulse IV. kg s−2 Choose the correct answer from the options given below: (1) A-IV, B-III, C-II, D-I (2) A-IV, B-III, C-I, D-II (3) A-III, B-IV, C-I, D-II (4) A-II, B-I, C-III, D-IV

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. 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. 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 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. 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 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. Dimension of 1 should be equal to μ0ε0 (1) L T−1 (2) T2 L−2 (3) L2 T−2 (4) T L−1

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. 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. 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. 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 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

Q4. A vehicle of mass 200 kg is moving along a levelled curved road of radius 70 m with angular velocity of 0 . 2 rad s-1. The centripetal force acting on the vehicle is: (1) 560 N (2) 2800 N (3) 2240 N (4) 14 N

Q4. A particle of mass 𝑚 moving with velocity 𝑣 collides with a stationary particle of mass 2𝑚. After collision, they stick together and continue to move together with velocity (1) 𝑣 (2) 𝑣 3 4 𝑣 (3) 𝑣 (4) 2

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. 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

Q6. A bullet of 10 g leaves the barrel of gun with a velocity of 600 m s−1 . If the barrel of gun is 50 cm long and mass of gun is 3 kg, then value of impulse supplied to the gun will be: (1) 6 N s (2) 3 N s (3) 36 N s (4) 12 N s

Q6. Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth 𝑑= 𝑅 from the 2 surface of earth, if its weight on the surface of earth is 200 N, will be : (Given 𝑅= radius of earth) (1) 300 N (2) 100 N (3) 400 N (4) 500 N

Q7. A wire of length L and radius r is clamped rigidly at one end. When the other end of the wire is pulled by a force f , its length increases by l. Another wire of same material of length 2L and radius 2r is pulled by a force 2f . Then the increase in its length will be: (1) 4l (2) 2l (3) 2l (4) l

Q8. The ratio of escape velocity of a planet to the escape velocity of earth will be:- Given: Mass of the planet is 16 times mass of earth and radius of the planet is 4 times the radius of earth. JEE Main 2023 (12 Apr Shift 1) JEE Main Previous Year Paper (1) 4 : 1 (2) 1 : 4 (3) 1 : √2 (4) 2 : 1 Q9. 64 identical drops each charged upto potential of 10 mV are combined to form a bigger drop. The potential of the bigger drop will be _____ mV .

Q8. A thermodynamic system is taken through cyclic process. The total work done in the process is : JEE Main 2023 (15 Apr Shift 1) JEE Main Previous Year Paper (1) 200 J (2) 300 J (3) 100 J (4) Zero

Q8. The height of liquid column raised in a capillary tube of certain radius when dipped in liquid 𝐴 vertically is, 5 cm. If the tube is dipped in a similar manner in another liquid 𝐵 of surface tension and density double the JEE Main 2023 (30 Jan Shift 1) JEE Main Previous Year Paper values of liquid 𝐴, the height of liquid column raised in liquid B would be ______ m. (1) 0 . 20 (2) 0 . 5 (3) 0 . 05 (4) 0 . 10