Practice Questions

Q4. The maximum and minimum distances of a comet from the Sun are 1. 6 × 1012 m and 8. 0 × 1010 m respectively. If the speed of the comet at the nearest point is 6 × 104 m s−1 , the speed at the farthest point is (1) 1. 5 × 103 m s−1 (2) 6. 6 × 103 m s−1 (3) 3. 0 × 103 m s−1 (4) 4. 5 × 103 m s−1

Q4. A block moving horizontally on a smooth surface with a speed of 40 m s-1 splits into two parts with masses in the ratio of 1 : 2 . If the smaller part moves at 60 m s-1 in the same direction, then the fractional change in kinetic energy is : 1 2 (1) (2) 3 3 1 1 (3) (4) 4 8

Q4. A boy reaches the airport and finds that the escalator is not working. He walks up the stationary escalator in time t1. If he remains stationary on a moving escalator then the escalator takes him up in time t2. The time taken by him to walk up on the moving escalator will be: (1) t1t2 (2) t1+t2 t2−t1 2 (3) t1t2 (4) t2 −t1 t2+t1

Q5. Four identical particles of equal masses 1 kg made to move along the circumference of a circle of radius 1 m under the action of their own mutual gravitational attraction. The speed of each particle will be: JEE Main 2021 (24 Feb Shift 1) JEE Main Previous Year Paper + 2√2 (1) √𝐺1 + 2√2 (2) √ 𝐺21 𝐺 2√2𝐺 (3) (4) √1 + √ 22√2 - 1 2

Q5. The minimum and maximum distances of a planet revolving around the Sun are 𝑥1 and 𝑥2. If the minimum speed of the planet on its trajectory is 𝑣0, then its maximum speed will be: (1) 𝑣0𝑥12 (2) 𝑣0𝑥22 𝑥22 𝑥12 𝑣0𝑥1 𝑣0𝑥2 (3) (4) 𝑥2 𝑥1

Q5. A system consists of two identical spheres each of mass 1 . 5 kg and radius 50 cm at the ends of a light rod. The distance between the centres of the two spheres is 5 m . What will be the moment of inertia of the system about an axis perpendicular to the rod passing through its midpoint? (1) 1 . 905 × 105 kg m2 (2) 18 . 75 kg m2 (3) 19 . 05 kg m2 (4) 1 . 875 × 105 kg m2

Q5. Moment of inertia of a square plate of side l about the axis passing through one of the corner and perpendicular to the plane of square plate is given by: (1) Ml26 (2) 23 Ml2 (3) Ml2 (4) Ml212

Q5. An automobile of mass m accelerates starting from the origin and initially at rest, while the engine supplies constant power P . The position is given as a function of time by: JEE Main 2021 (27 Jul Shift 2) JEE Main Previous Year Paper 1 1 2 (1) 3 (2) t 2 t 3 ( 89Pm ) 2 ( 98Pm ) 2 1 1 3 (3) 3 (4) t 2 t 2 ( 9m8P ) 2 ( 98Pm ) 2

Q5. Four equal masses, m each are placed at the corners of a square of length (l) as shown in the figure. The moment of inertia of the system about an axis passing through A and parallel to DB would be : JEE Main 2021 (16 Mar Shift 1) JEE Main Previous Year Paper (1) ml2 (2) 2 ml2 (3) 3 ml2 (4) √3 ml2

Q5. The time period of a satellite in a circular orbit of the radius R is T. The period of another satellite in a circular orbit of the radius 9R is: (1) 9T (2) 27T (3) 12T (4) 3T

Q5. Four identical solid spheres each of mass m and radius a are placed with their centres on the four corners of a square of side b. The moment of inertia of the system about one side of square where the axis of rotation is parallel to the plane of the square is : (1) 85 ma2 + mb2 (2) 54 ma2 + 2mb2 (3) 85 ma2 + 2mb2 (4) 54 ma2

Q5. The figure shows two solid discs with radius R and r respectively. If mass per unit area is the same for both, what is the ratio of MI of bigger disc around axis AB (Which is ⊥ to the plane of the disc and passing through its centre) of MI of smaller disc around one of its diameters lying on its plane? Given M is the mass of the larger disc. ( MI stands for a moment of inertia) (1) R2 : r2 (2) 2r4 : R4 (3) 2R2 : r2 (4) 2R4 : r4

Q5. A body of mass 𝑚 dropped from a height ℎ reaches the ground with a speed of 0 . 8√𝑔ℎ. The value of work done by the air-friction is: (1) -0 . 68𝑚𝑔ℎ (2) 𝑚𝑔ℎ (3) 0 . 64𝑚𝑔ℎ (4) 1 . 64𝑚𝑔ℎ

Q5. Two satellites A and B of masses 200 kg and 400 kg are revolving round the earth at height of 600 km and 1600 km respectively. If TA and TB are the time periods of A and B respectively then the value of TB −TA : [ Given : radius of earth = 6400 km, mass of earth = 6 × 1024 kg ] (1) 4. 24 × 103 s (2) 3. 33 × 102 s (3) 1. 33 × 103 s (4) 4. 24 × 102 s

Q5. Two narrow bores of diameter 5. 0 mm and 8. 0 mm are joined together to form a U−shaped tube open at both ends. If this U−tube contains water, what is the difference in the level of two limbs of the tube. [Take surface tension of water T = 7. 3 × 10−2 N m−1 , angle of contact = 0, g = 10 m s−2 and density of water = 1. 0 × 103 kg m−3] (1) 5. 34 mm (2) 3. 62 mm (3) 2. 19 mm (4) 4. 97 mm JEE Main 2021 (26 Aug Shift 1) JEE Main Previous Year Paper

Q5. The instantaneous velocity of a particle moving in a straight line is given as v = αt + βt2 , where α and β are constants. The distance travelled by the particle between 1 s and 2 s is: (1) 3α + 7β (2) 32 α + 73 β (3) α 2 + β3 (4) 32 α + 72 β Q6. → A force F = + N acts on a body of mass 5 kg. If the body starts from rest, its position vector →rat (40ˆi 10ˆj) time t = 10 s will be + + m (1) (100ˆi 400ˆj) m (2) (100ˆi 100ˆj) + + m (3) (400ˆi 100ˆj) m (4) (400ˆi 400ˆj)

Q5. If the kinetic energy of a moving body becomes four times its initial kinetic energy, then the percentage change in its momentum will be: (1) 100% (2) 200% (3) 300% (4) 400%

Q5. Consider a situation in which a ring, a solid cylinder and a solid sphere roll down on the same inclined plane without slipping. Assume that they start rolling from rest and having identical diameter. The correct statement for this situation is (1) The sphere has the greatest and the ring has the (2) The ring has the greatest and the cylinder has the least velocity of the centre of mass at the bottom least velocity of the centre of mass at the bottom of the inclined plane. of the inclined plane. (3) All of them will have same velocity. (4) The cylinder has the greatest and the sphere has the least velocity of the centre of mass at the bottom of the inclined plane.

Q5. What will be the nature of flow of water from a circular tap, when its flow rate increased from 0. 18 L (min)−1 to 0. 48 L (min)−1? The radius of the tap and viscosity of water are 0. 5 cm and 10−3 Pa s, respectively. (Density of water : 103 kg m−3 ) JEE Main 2021 (16 Mar Shift 2) JEE Main Previous Year Paper (1) Unsteady to steady flow (2) Remains steady flow (3) Remains turbulent flow (4) Steady flow to unsteady flow

Q5. The boxes of masses 2 kg and 8 kg are connected by a massless string passing over smooth pulleys. Calculate the time taken by box of mass 8 kg to strike the ground starting from rest. (g = 10 m s−2) (1) 0. 25 s (2) 0. 34 s (3) 0. 2 s (4) 0. 4 s JEE Main 2021 (27 Aug Shift 2) JEE Main Previous Year Paper

Q5. A geostationary satellite is orbiting around an arbitrary planet P at a height of 11R above the surface of P , R being the radius of P . The time period of another satellite in hours at a height of 2R from the surface of P is ________ has the time period of 24 hours. (1) 6√2 (2) 6 √2 (3) 3 (4) 5

Q5. Consider a uniform wire of mass M and length L. It is bent into a semicircle. Its moment of inertia about a line perpendicular to the plane of the wire passing through the centre is : (1) 1 ML2 (2) 2 ML2 4 π2 5 π2 (3) ML2 (4) 1 ML2 π2 2 π2

Q6. Two stars of masses 𝑚 and 2𝑚 at a distance 𝑑 rotate about their common centre of mass in free space. The period of revolution is 2𝜋√ (1) 2𝜋√𝑑3 (2) 3𝐺𝑚 𝑑3 3𝐺𝑚 (3) 1 3𝐺𝑚 (4) 1 2𝜋√ 𝑑3 2𝜋√𝑑33𝐺𝑚

Q6. In Millikan's oil drop experiment, what is viscous force acting on an uncharged drop of radius 2. 0 × 10−5 m and density 1. 2 × 103 kg m−3 ? Take viscosity of liquid = 1. 8 × 10−5 N s m−2. (Neglect buoyancy due to air). (1) 5. 8 × 10−10 N (2) 3. 9 × 10−10 N (3) 1. 8 × 10−10 N (4) 3. 8 × 10−11 N

Q6. Two wires of same length and radius are joined end to end and loaded. The Young's moduli of the materials of the two wires are 𝑌1 and 𝑌2. The combination behaves as a single wire then its Young's modulus is: (1) 𝑌= 2𝑌1𝑌2 (2) 𝑌= 2𝑌1𝑌2 3𝑌1 + 𝑌2 𝑌1 + 𝑌2 𝑌1𝑌2 𝑌1𝑌2 (3) 𝑌= (4) 𝑌= 2𝑌1 + 𝑌2 𝑌1 + 𝑌2