Practice Questions

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 system of two blocks of masses m = 2 kg and M = 8 kg is placed on a smooth table as shown in figure. The coefficient of static friction between two blocks is 0. 5 . The maximum horizontal force F that can be applied to the block of mass M so that the blocks move together will be (g = 9. 8 m s−2) (1) 9. 8 N (2) 39. 2 N (3) 49 N (4) 78. 4 N

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. When a ball is dropped into a lake from a height 4. 9 m above the water level, it hits the water with a velocity v and then sinks to the bottom with the constant velocity v . It reaches the bottom of the lake 4. 0 s after it is dropped. The approximate depth of the lake is (1) 39. 2 m (2) 19. 6 m (3) 73. 5 m (4) 29. 4 m

Q4. Sand is being dropped from a stationary dropper at a rate of 0. 5 kg s−1 on a conveyor belt moving with a velocity of 5 m s−1 . The power needed to keep belt moving with the same velocity will be (1) 1. 25 W (2) 2. 5 W (3) 6. 25 W (4) 12. 5 W

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 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. Two bodies of masses 𝑚1 = 5 kg and 𝑚2 = 3 kg are connected by a light string going over a smooth light pulley on a smooth inclined plane as shown in the figure. The system is at rest. The force exerted by the inclined plane on the body of mass 𝑚1 will be : [Take 𝑔= 10 m s-2] ​ (1) 30 N (2) 40 N (3) 50 N (4) 60 N

Q4. As per the given figure, two blocks each of mass 250 g are connected to a spring of spring constant 2 N m−1 . If both are given velocity v in opposite directions, then maximum elongation of the spring is (1) v (2) v 2√2 2 (3) v (4) v 4 √2

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. A block of mass M slides down on a rough inclined plane with constant velocity. The angle made by the incline plane with horizontal is θ. The magnitude of the contact force will be : (1) Mg (2) Mg cos θ (3) √Mg sin θ + Mg cos θ (4) Mg sin θ√1 + μ

Q4. Potential energy as a function of r is given by U = A −B , where r is the interatomic distance, A and B are r10 r5 positive constants. The equilibrium distance between the two atoms will be : (1) A 15 (2) B 15 ( B ) ( A ) (3) 2A 15 (4) B 15 ( B ) ( 2A )

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 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. 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. 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. The height of any point 𝑃 above the surface of earth is equal to diameter of earth. The value of acceleration due to gravity at point 𝑃 will be : (Given 𝑔= acceleration due to gravity at the surface of earth). (1) 𝑔 (2) 𝑔 2 4 𝑔 𝑔 (3) (4) 3 9

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. 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. 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. 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 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. 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 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. 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