Practice Questions

Q4. A bag of sand of mass 9. 8 kg is suspended by a rope. A bullet of 200 g travelling with speed 10 ms−1 gets embedded in it, then loss of kinetic energy will be (1) 4. 9 J (2) 9. 8 J (3) 14. 7 (4) 19. 6 J

Q4. A bullet of mass 200 g having initial kinetic energy 90 J is shot inside a long swimming pool as shown in the figure. If it's kinetic energy reduces to 40 J within 1 s, the minimum length of the pool, the bullet has to travel so that it completely comes to rest is (1) 45m (2) 90m (3) 125m (4) 25m

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. 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 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. 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 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. 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. 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 solid cylinder and a solid sphere, having same mass 𝑀 and radius 𝑅, roll down the same inclined plane from top without slipping. They start from rest. The ratio of velocity of the solid cylinder to that of the solid sphere, with which they reach the ground, will be (1) 5 (2) 4 √ 3 √ 5 (3) 3 (4) 14 √ 5 √ 15

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. 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

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. A solid metallic cube having total surface area 24 m2 is uniformly heated. If its temperature is increased by 10°C, calculate the increase in volume of the cube. (Given 𝛼= 5 . 0 × 10-4∘C-1). (1) 2 . 4 × 106 cm3 (2) 1 . 2 × 105 cm3 (3) 6 × 104 cm3 (4) 4 . 8 × 105 cm3

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 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

Q6. The torque of a force 5 ^𝑖+ 3 ^𝑗- 7 ^𝑘 about the origin is 𝜏. If the force acts on a particle whose position vector is 2 ^𝑖+ 2 ^𝑗+ ^𝑘, then the value of 𝜏 will be (1) 11 ^𝑖+ 19 ^𝑗- 4 ^𝑘 (2) -11 ^𝑖+ 9 ^𝑗- 16 ^𝑘 (3) -17 ^𝑖+ 19 ^𝑗- 4 ^𝑘 (4) 17 ^𝑖+ 9 ^𝑗+ 16 ^𝑘

Q6. Two cylindrical vessels of equal cross-sectional area 16 cm2 contain water upto heights 100 cm and 150 cm respectively. The vessels are interconnected so that the water levels in them become equal. The work done by the force of gravity during the process, is [Take density of water = 103 kg m−3 and g = 10 ms−2 ] (1) 0. 25 J (2) 1 J (3) 8 J (4) 12 J JEE Main 2022 (27 Jul Shift 1) JEE Main Previous Year Paper

Q6. A pressure-pump has a horizontal tube of cross-sectional area 10 cm2 for the outflow of water at a speed of 20 m s−1 . The force exerted on the vertical wall just in front of the tube which stops water horizontally flowing out of the tube, is: [given : density of water = 1000 kg m−3 ] (1) 300 N (2) 500 N (3) 250 N (4) 400 N

Q6. A stone tide to a string of length L is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of change in its velocity, as it reaches a position where the string is horizontal, is √x(u2 −gL). The value of x is (1) 2 (2) 3 (3) 4 (4) 1

Q6. The approximate height from the surface of earth at which the weight of the body becomes 1 of its weight on 3 the surface of earth is : [Radius of earth R = 6400 km and √3 = 1. 732 ] (1) 3840 km (2) 4685 km (3) 2133 km (4) 4267 km

Q6. The time period of a satellite revolving around earth in a given orbit is 7 hours. If the radius of orbit is increased to three times its previous value, then approximate new time period of the satellite will be (1) 36 hours (2) 40 hours (3) 30 hours (4) 25 hours JEE Main 2022 (29 Jun Shift 2) JEE Main Previous Year Paper

Q6. The length of a seconds pendulum at a height h = 2R from earth surface will be: (Given: R = Radius of earth and acceleration due to gravity at the surface of earth g = π2 m s−2 ) (1) 9 2 m (2) 49 m (3) 8 9 m (4) 19 m

Q6. A body of mass m is projected with velocity λve in vertically upward direction from the surface of the earth into space. It is given that ve is escape velocity and λ < 1 . If air resistance is considered to the negligible, then the maximum height from the centre of earth, to which the body can go, will be ( R : radius of earth) (1) R (2) R 1+λ2 1−λ2 (3) R (4) λ2R 1−λ 1−λ2

Q6. A water drop of diameter 2 cm is broken into 64 equal droplets. The surface tension of water is 0. 075 N m−1 . In this process the gain in surface energy will be (1) 2. 8 × 10−4 J (2) 1. 5 × 10−3 J (3) 1. 9 × 10−4 J (4) 9. 4 × 10−5 J