Practice Questions

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. 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. Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A : An electric fan continues to rotate for some time after the current is switched off. Reason R: Fan continues to rotate due to inertia of motion. In the light of above statements, choose the most appropriate answer from the options given below. (1) A is correct but R is not correct (2) A is not correct but R is correct (3) Both A and R are correct and R is the correct (4) Both A and R are correct but R is NOT the explanation of A correct explanation of A

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. 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. 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. 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 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

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 bullet of mass 0. 1 kg moving horizontally with speed 400 m s−1 hits a wooden block of mass 3. 9 kg kept on a horizontal rough surface. The bullet gets embedded into the block and moves 20 m before coming to rest. The coefficient of friction between the block and the surface is _______. (1) 0. 90 (2) 0. 50 (3) 0. 65 (4) 0. 25

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. Two projectiles A and B are thrown with initial velocities of 40 m s−1 and 60 m s−1 at angles 30° and 60° with the horizontal respectively. The ratio of their ranges respectively is (g = 10 m s−2) (1) 4 : 9 (2) 2 : √3 (3) √3 : 2 (4) 1 : 1 m s−1 . If the force acting on the

Q4. A body of mass (5 ± 0. 5) kg is moving with a velocity of (20 ± 0. 4) m s−1. Its kinetic energy will be (1) (1000 ± 0. 14) J (2) (500 ± 0. 14) J (3) (500 ± 140) J (4) (1000 ± 140) J

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

Q4. A car is moving on a horizontal curved road with radius 50 m. The approximate maximum speed of car will be, if friction between tyres and road is 0. 34. [Take g = 10 m s−2 ] (1) 3. 4 m s−1 (2) 22. 4 m s−1 (3) 13 m s−1 (4) 17 m s−1

Q4. A body of mass 200 g is tied to a spring of spring constant 12. 5 N m−1 , while the other end of spring is fixed at point O. If the body moves about O in a circular path on a smooth horizontal surface with constant angular speed 5 rad s−1 , then the ratio of extension in the spring to its natural length will be : (1) 1 : 2 (2) 1 : 1 (3) 2 : 3 (4) 2 : 5 Q5. → + N , where ˆi A body of mass 1 kg begins to move under the action of a time dependent force F = (tˆi 3t2ˆj) and ˆj are the unit vectors along x and y axis. The power developed by above force, at the time t = 2 s , will be _______ W.

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. 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 car is moving with a constant speed of 20 m s−1 in a circular horizontal track of radius 40 m. A bob is suspended from the roof of the car by a massless string. The angle made by the string with the vertical will be : (Take g = 10 m s−2 ) (1) π (2) π 6 2 (3) π (4) π 4 3

Q4. A stone tied to 180 cm long string at its end is making 28 revolutions in horizontal circle in every minute. The magnitude of acceleration of stone is 1936 x m s−2 . The value of x ______. [Take π = 227 ]

Q4. Given below are two statements: Statement I : A truck and a car moving with same kinetic energy are brought to rest by applying breaks which provide equal retarding forces. Both come to rest in equal distance. Statement II : A car moving towards east takes a turn and moves towards north, the speed remains unchanged. The acceleration of the car is zero. In the light of given statements, choose the most appropriate answer from the options given below (1) Statement I is correct but statement II is incorrect (2) Statement I is incorrect but statement II is correct (3) Both statement I and Statement II are correct (4) Both statement I and statement II are incorrect

Q4. As per the given figure, a small ball 𝑃 slides down the quadrant of a circle and hits the other ball 𝑄 of equal mass which is initially at rest. Neglecting the effect of friction and assume the collision to be elastic, the velocity of ball 𝑄 after collision will be : ( 𝑔 = 10 m s-2 ) (1) 0 (2) 0 . 25 m s-1 (3) 2 m s-1 (4) 4 m s-1

Q4. A car is moving on a circular path of radius 600 m such that the magnitudes of the tangential acceleration and centripetal acceleration are equal. The time taken by the car to complete first quarter of revolution, if it is 2 ) s . The value of t is ______. moving with an initial speed of 54 km h−1 is t(1–e– π

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 block of mass 5 kg is placed at rest on a table of rough surface. Now, if a force of 30 N is applied in the direction parallel to surface of the table, the block slides through a distance of 50 m in an interval of time 10 s. Coefficient of kinetic friction is (given, 𝑔 = 10 m s – 2 ): (1) 0 . 60 (2) 0 . 75 (3) 0 . 50 (4) 0 . 25 𝑣𝑒