Practice Questions

Q4. Consider two satellites 𝑆1 and 𝑆2 with periods of revolution 1hr and 8hr respectively revolving around a planet in circular orbits. The ratio of angular velocity of satellite 𝑆1 to the angular velocity of satellite 𝑆2 is: (1) 8: 1 (2) 2: 1 (3) 1: 4 (4) 1: 8

Q4. A porter lifts a heavy suitcase of mass 80 kg and at the destination lowers it down by a distance of 80 cm with a constant velocity. Calculate the work done by the porter in lowering the suitcase. (take g = 9. 8 ms−2 ) (1) −62720. 0 J (2) −627. 2 J (3) +627. 2 J (4) 784. 0 J

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. An object of mass m1 collides with another object of mass m2 , which is at rest. After the collision the objects move with equal speeds in opposite direction. The ratio of the masses m2 : m1 is : (1) 3 : 1 (2) 2 : 1 (3) 1 : 2 (4) 1 : 1

Q4. A block of mass 𝑚 slides on the wooden wedge, which in turn slides backward on the horizontal surface. The acceleration of the block with respect to the wedge is: Given 𝑚= 8 kg, 𝑀= 16 kg Assume all the surfaces shown in the figure to be frictionless. 3 4 (1) g (2) g 5 3 6 2 (3) g (4) 5 3g

Q4. List- I List- II (a) MI of the rod (length L, Mass M, about an axis ⊥ to the rod passing (i) through the midpoint) 8ML2 3 (b) MI of the rod (length L, Mass 2M, about an axis ⊥ to the rod ML2 (ii) 3 passing through one of its end) (c) MI of the rod (length 2L, Mass M, about an axis ⊥ to the rod (iii) passing through its midpoint) ML2 12 (d) MI of the rod (Length 2L, Mass 2M, about an axis ⊥ to the rod (iv) passing through one of its end) 2ML2 3 Choose the correct answer from the options given below: JEE Main 2021 (27 Jul Shift 1) JEE Main Previous Year Paper (1) (a) −(ii), (b) −(iii), (c) −(i), (d) −(iv) (2) (a) −(ii), (b) −(i), (c) − (iii), (d) −(iv) (3) (a) −(iii), (b) −(iv), (c) − (ii), (d) −(i) (4) (a) − (iii), (b) −(iv), (c) −(i), (d) −(ii)

Q4. Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Moment of inertia of a circular disc of mass 𝑀 and radius 𝑅 about 𝑋, 𝑌 axes (passing through its plane) and Z-axis which is perpendicular to its plane were found to be 𝐼x, 𝐼y and 𝐼z, respectively. The respective radii of gyration about all the three axes will be the same. Reason R: A rigid body making rotational motion has fixed mass and shape. In the light of the above statements, choose the most appropriate answer from the options given below: (1) Both A and R are correct but R is not the correct (2) A is not correct but R is correct. explanation of A. (3) A is correct but R is not correct. (4) Both A and R are correct and R is the correct explanation of A.

Q4. A particle of mass m is suspended from a ceiling through a string of length L. The particle moves in a horizontal circle of radius r such that r = L . The speed of particle will be : √2 (1) √rg (2) √2rg (3) √rg2 (4) 2√rg

Q4. Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Body P having mass M moving with speed u has head-on collision elastically with another body Q having mass m initially at rest. If m ≪M , body Q will have a maximum speed equal to 2u after collision. Reason R : During elastic collision, the momentum and kinetic energy are both conserved. In the light of the above statements, choose the most appropriate answer from the options given below: (1) A is correct but R is not correct. (2) A is not correct but R is correct. (3) Both A and R are correct and R is the correct (4) Both A and R are correct but R is NOT the correct explanation of A explanation of A

Q4. A body of mass M moving at speed V0 collides elastically with a mass m at rest. After the collision, the two masses move at angles θ1 and θ2 with respect to the initial direction of motion of the body of mass M.. The largest possible value of the ratio M m , for which the angles θ1 and θ2 will be equal, is : (1) 3 (2) 4 (3) 2 (4) 1

Q4. The trajectory of a projectile in a vertical plane is y = αx −βx2, where α and β are constants and x & y are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection θ and the maximum height attained H are respectively given by (1) tan−1 α, 4α2β (2) tan−1( αβ ), α2β (3) tan−1 β, α22β (4) tan−1 α, α24β

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

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. Given below is the plot of a potential energy function U(x) for a system, in which a particle is in one dimensional motion, while a conservative force F(x) acts on it. Suppose that Emech = 8 J, the incorrect statement for this system is : (1) at x > x4, K. E . is constant throughout the (2) at x < x1, K. E . is smallest and the particle is region. moving at the slowest speed. (3) at x = x2, K. E . is greatest and the particle is (4) at x = x3, K. E. = 4 J moving at the fastest speed.

Q4. Inside a uniform spherical shell : (a) The gravitational field is zero. (b) The gravitational potential is zero. (c) The gravitational field is the same everywhere. (d) The gravitation potential is the same everywhere. (e) All the above. Choose the most appropriate answer from the options given below: (1) (a), (c) and (d) only (2) (a), (b) and (c) only (3) (b), (c) and (d) only (4) (e) only

Q4. Thermodynamic process is shown below on a P −V diagram for one mole of an ideal gas. If V2 = 2V1 , then the ratio of temperature T2 is : T1 (1) √2 (2) 1 √2 (3) 1 (4) 2 2

Q4. A balloon was moving upwards with a uniform velocity of 10 m s−1 . An object of finite mass is dropped from the balloon when it was at a height of 75 m from the ground level. The height of the balloon from the ground when object strikes the ground was around: (takes the value of g as 10 m s−2 ) (1) 300 m (2) 200 m (3) 125 m (4) 250 m

Q4. A body weighs 49 N on a spring balance at the north pole. What will be its weight recorded on the same weighing machine, if it is shifted to the equator? [Use g = GM = 9. 8 m s−2 and radius of earth, R = 6400 km.] R2 (1) 49. 17 N (2) 48. 83 N (3) 49. 83 N (4) 49 N

Q4. A thin circular ring of mass M and radius r is rotating about its axis with an angular speed ω. Two particles having mass m each are now attached at diametrically opposite points. The angular speed of the ring will become: (1) ω M (2) ω M+2M m M+m M m M−2 (3) ω (4) ω m m M+2 M+2

Q4. A sphere of mass 2 kg and radius 0. 5 m is rolling with an initial speed of 1 m s−1 goes up an inclined plane which makes an angle of 30° with the horizontal plane, without slipping. How low will the sphere take to return to the starting point A ? (1) 0. 60 s (2) 0. 52 s (3) 0. 56 s (4) 0. 80 s

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. 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. 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. A person whose mass is 100 kg travels from Earth to Mars in a spaceship. Neglect all other objects in sky and take acceleration due to gravity on the surface of the Earth and Mars as 10 m s−2 and 4 m s−2 , respectively. Identify from the below figures, the curve that fits best for the weight of the passenger as a function of time. JEE Main 2021 (20 Jul Shift 1) JEE Main Previous Year Paper (1) (c) (2) (a) (3) (d) (4) (b)

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.