Practice Questions

Q4. A body of mass 8 kg and another of mass 2 kg are moving with equal kinetic energy. The ratio of their respective momenta will be (1) 1: 1 (2) 2: 1 (3) 1: 4 (4) 4: 1

Q4. Water falls from a 40 m high dam at the rate of 9 × 104 kg per hour. Fifty percentage of gravitational potential energy can be converted into electrical energy. Using this hydro electric energy number of 100 W lamps, that can be lit, is (Take g = 10 ms−2 ) (1) 25 (2) 50 (3) 100 (4) 18

Q4. A block of metal weighing 2 kg is resting on a frictionless plane (as shown in figure). It is struck by a jet releasing water at a rate of 1 kg s−1 and at a speed of 10 m s−1 . Then, the initial acceleration of the block, in m s−2 , will be (1) 3 (2) 6 (3) 5 (4) 4

Q4. For a particle in uniform circular motion, the acceleration →𝑎 at any point 𝑃𝑅, 𝜃 on the circular path of radius 𝑅 is (when 𝜃 is measured from the positive 𝑥-axis and 𝑣 is uniform speed): (1) 𝑣2 𝑣2 (2) 𝑣2 𝑣2 - ^i + ^j - ^i + ^j 𝑅sin𝜃 𝑅cos𝜃 𝑅cos𝜃 𝑅sin𝜃 (3) 𝑣2 𝑣2 (4) 𝑣2 𝑣2 - ^i - ^j - ^i + ^j 𝑅cos𝜃 𝑅sin𝜃 𝑅 𝑅

Q4. If force →F = 3 ^𝑖+ 4 ^𝑗- 2 ^𝑘 acts on a particle having position vector 2 ^𝑖+ ^𝑗+ 2 ^𝑘 then, the torque about the origin will be: (1) -10 ^i + 10 ^j + 5 ^k (2) 3 ^i + 4 ^j - 2 ^k (3) 10 ^i + 5 ^j - 10 ^k (4) 10 ^i + ^j - 5 ^k

Q4. A block of mass 10 kg starts sliding on a surface with an initial velocity of 9. 8 ms−1 . The coefficient of friction between the surface and block is 0. 5 . The distance covered by the block before coming to rest is :[use g = 9. 8 ms−2 ] (1) 9. 8 m (2) 4. 9 m (3) 12. 5 m (4) 19. 6 m →Q5. + x −y plane. Assume distance in A particle experiences a variable force F = (4xˆi 3y2ˆj) in a horizontal meters and force is newton. If the particle moves from point (1, 2) to point (2, 3) in the x −y plane, then Kinetic Energy changes by : (1) 25 J (2) 50 J (3) 12. 5 J (4) 0 J

Q4. A body of mass 0 . 5 kg travels on straight line path with velocity 𝑣= 3𝑥2 + 4 m s-1. The net work done by the force during its displacement from 𝑥= 0 to 𝑥= 2 m is (1) 64 J (2) 60 J (3) 120 J (4) 128 J

Q5. If momentum of a body is increased by 20%, then its kinetic energy increases by : (1) 36% (2) 40% (3) 44% (4) 48%

Q5. A particle of mass 500 g is moving in a straight line with velocity v = bx 52 . The work done by the net force during its displacement from x = 0 to x = 4 m is (Take b = 0. 25 m −32 s−1 ). (1) 2 J (2) 4 J (3) 8 J (4) 16 J

Q5. A fly wheel is accelerated uniformly from rest and rotates through 5 rad in the first second. The angle rotated by the fly wheel in the next second, will be : (1) 7. 5 rad (2) 15 rad (3) 20 rad (4) 30 rad

Q5. A thin circular ring of mass M and radius R is rotating with a constant angular velocity 2 rad s−1 in a horizontal plane about an axis vertical to its plane and passing through the center of the ring. If two objects each of mass m be attached gently to the opposite ends of a diameter of ring, the ring will then rotate with an angular velocity (in rad s−1 ). (1) M (2) (M+2m) (M+m) 2M (3) 2M (4) 2(M+2m) (M+2m) M JEE Main 2022 (26 Jun Shift 1) JEE Main Previous Year Paper

Q5. The percentage decrease in the weight of a rocket, when taken to a height of 32 km above the surface of earth will, be (Radius of earth = 6400 km) (1) 1% (2) 3% (3) 4% (4) 0. 5%

Q5. If the radius of earth shrinks by 2% while its mass remains same. The acceleration due to gravity on the earth's surface will approximately (1) decrease by 2% (2) decrease by 4% (3) increase by 2% (4) increase by 4%

Q5. Two planets A and B of equal mass are having their period of revolutions TA and TB such that TA = 2TB . These planets are revolving in the circular orbits of radii rA and rB respectively. Which out of the following would be the correct relationship of their orbits? (1) 2r2A = r3B (2) r3A = 2r3B (3) r3A = 4r3B (4) T A2 −T B2 = GMπ2 (r3B −4r3A)

Q5. Two satellites A and B having masses in the ratio 4 : 3 are revolving in circular orbits of radii 3r and 4r respectively around the earth. The ratio of total mechanical energy of A to B is (1) 9 : 16 (2) 16 : 9 (3) 1 : 1 (4) 4 : 3

Q5. In the given figure, the block of mass m is dropped from the point ′A′ . The expression for kinetic energy of block when it reaches point ′B′ is (1) mgy0 (2) 12 mgy20 (3) 1 mgy2 (4) mg(y −y0) 2

Q5. Assume there are two identical simple pendulum Clocks- 1 is placed on the earth and Clock- 2 is placed on a space station located at a height h above the earth surface. Clock- 1 and Clock- 2 operate at time periods 4 s and 6 s respectively. Then the value of h is - (consider radius of earth RE = 6400 km and g on earth 10 m s−2 ) (1) 1200 km (2) 1600 km (3) 3200 km (4) 4800 km JEE Main 2022 (28 Jul Shift 2) JEE Main Previous Year Paper

Q5. A √34 m long ladder weighing 10 kg leans on a frictionless wall. Its feet rest on the floor 3 m away from the wall as shown in the figure. If Ff and Fw are the reaction forces of the floor and the wall, then ratio of Fw will Ff be : (Use g = 10 m s−2 .) (1) 6 (2) 3 √110 √113 (3) 3 (4) 2 √109 √109

Q5. Two billiard balls of mass 0. 05 kg each moving in opposite directions with 10 ms−1 collide and rebound with the same speed. If the time duration of contact is t = 0. 005 s, then what is the force exerted on the ball due to each other? (1) 100 N (2) 200 N (3) 300 N (4) 400 N

Q5. A smooth circular groove has a smooth vertical wall as shown in figure. A block of mass m moves against the wall with a speed v . Which of the following curve represents the correct relation between the normal reaction on the block by the wall (N) and speed of the block (v)? (1) (2) (3) (4) JEE Main 2022 (29 Jul Shift 1) JEE Main Previous Year Paper

Q5. One end of a massless spring of spring constant k and natural length l0 is fixed while the other end is connected to a small object of mass m lying on a frictionless table. The spring remains horizontal on the table. If the object is made to rotate at an angular velocity ω about an axis passing trough fixed end, then the elongation of the spring will be (1) k−mω2l0 (2) mω2l0 mω2 k+mω2 (3) mω2l0 (4) k+mω2l0 k−mω2 mω2

Q5. A body is projected vertically upwards from the surface of earth with a velocity equal to one third of escape velocity. The maximum height attained by the body will be (Take radius of earth = 6400 km and 𝑔= 10 ms-2) (1) 800 km (2) 1600 km (3) 2133 km (4) 4800 km

Q5. Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R. JEE Main 2022 (26 Jun Shift 2) JEE Main Previous Year Paper Assertion A: If we move from poles to equator, the direction of acceleration due to gravity of earth always points towards the center of earth without any variation in its magnitude. Reason R: At equator, the direction of acceleration due to the gravity is towards the center of earth. In the light of above statements, choose the correct answer from the options given below (1) Assertion and reason both are correct and reason (2) Assertion and reason both are correct but reason is correct explanation of assertion. is not correct explanation of assertion. (3) Assertion is true but reason is false (4) Assertion is false but reason is true

Q5. Two blocks of masses 10 kg and 30 kg are placed on the same straight line with coordinates (0, 0) cm and (x, 0) cm respectively. The block of 10 kg is moved on the same line through a distance of 6 cm towards the other block. The distance through which the block of 30 kg must be moved to keep the position of centre of mass of the system unchanged is (1) 4 cm towards the 10 kg block (2) 2 cm away from the 10 kg block (3) 2 cm towards the 10 kg block (4) 4 cm away from the 10 kg block

Q5. A block A takes 2 s to slide down a frictionless incline of 30° and length l, kept inside a lift going up with uniform velocity v. If the incline is changed to 45° , the time taken by the block, to slide down the incline, will be approximately: (1) 2. 66 s (2) 0. 83 s (3) 1. 68 s (4) 0. 70 s