Practice Questions

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 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. 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. 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 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 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 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. 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. 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 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. 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 (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 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

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: An elevator can go up or down with uniform speed when its weight is balanced with the tension of its cable. Statement-II: Force exerted by the floor of an elevator on the foot of a person standing on it is more than his/her weight when the elevator goes down with increasing speed. In the light of the above statements, choose the correct answer from the options given below: (1) Both Statement I and Statement II are false (2) Statement I is true but Statement II is false (3) Both Statement I and Statement II are true (4) Statement I is false but Statement II is true

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. 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 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. 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 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. An average force of 125 N is applied on a machine gun firing bullets each of mass 10 g at the speed of 250 m s-1 to keep it in position. The number of bullets fired per second by the machine gun is : (1) 50 (2) 25 (3) 100 (4) 5 𝜌

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