Tiêu đề Gravitation-1.pdf ✅

Exercise 1: NCERT Based Topic-wise MCQs 1. Which of the following astronomers proposed a definitive model in which the planets moved in circles around a fixed central sun? NCERT Page-184 / N-127 (a) Copernicus (b) Kepler (c) Galileo (d) None of these 2. For elliptical orbits, in the equation T 2 = ( 4π 2 GMs ) R 3 R refers to NCERT Page-184 / N-129 (a) radius of orbit (c) semi-minor axis (b) major axis (d) semi-major axis 3. In planetary motion (a) the angular speed remains constant (b) the total angular momentum remains constant (c) the linear speed remains constant (d) neither the angular momentum nor angular speed remains constant 4. Kepler's second law may be stated as "under the influence of central force, in equal interval of time, position vector sweeps out equal NCERT Page-184/ N-128 (a) distance (b) area (c) displacement (d) volume 5. The figure shows a planet in elliptical orbit around the sun S. Where is the kinetic energy of the planet maximum? NCERT PAGE- 185 (a) P1 (b) P2 (c) P3 (d) P4 6. A planet revolves about the sun in elliptical orbit. The areal velocity ( dA dt) of the planet is 4.0 × 1016 m2 /s. The least distance between planet and the sun is 2 × 1012 m. Then the maximum speed of the planet in km/s is NCERT Page-185 / N-129 (a) 10 (b) 20 (c) 30 (d) 40 CHAPTER 9 GRAVITATION 9.1 INTRODUCTION 9. 2 KEPLER’S LAWS
7. In planetary motion the areal velocity of position vector of a planet depends on angular velocity (ω) and the distance of the planet from sun (r). If so, the correct relation for areal velocity is NCERT Page-185 / N-129 (a) dA dt ∝ ωr (b) dA dt ∝ ω 2 r (c) dA dt ∝ ωr 2 (d) dA dt ∝ √ωr 8. A planet goes round the sun three times as fast as the earth. If rp and re are the radii of orbit of the planet and the earth respectively then NCERT Page-184 / N-128 (a) re 3 = 8rp 3 (b) re 3 = 3rp 3 (c) re 3 = 9rp 3 (d) re 3 = 1 3 rp 3 9. The maximum and minimum distances of a comet from the sun are 8 × 1012 m and 1.6 × 1012 m. If its velocity when nearest to the sun is 60 m/s, what will be its velocity in m/s when it is farthest (a) 12 NCERT Page-185 / N-129 (b) 60 (c) 112 (d) 6 10. The period of moon's rotation around the earth is nearly 29 days. If moon's mass were 2 fold its present value and all other things remain unchanged, the period of moon's rotation would be nearly (a) 29√2 days NCERT Page-184, 185 / N-129 (b) 29/√2 days (c) 29 × 2 days (d) 29 days 11. 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 (a) 40 hours NCERT Page-184 / N-129 (b) 36 hours (c) 30 hours (d) 25 hours 12. Which of the following graphs represents the motion of a planet moving about the sun? NCERT Page-184/N-128
13. The figure shows elliptical orbit of a planet m about the sun S. The shaded area SCD is twice the shaded area SAB. If t1 is the time for the planet to move from C to D and t2 is the time to move from A to B then NCERT Page-184 / N-128, 129 (a) t1 = 4t2 (b) t1 = 2t2 (c) t1 = t2 (d) t1 > t2 14. If the distance of earth is halved from the sun, then the no. of days in a year will be NCERT Page-184 / N-129 (a) 365 (b) 182.5 (c) 730 (d) 129 15. If the earth is at one-fourth of its present distance from the sun, the duration of the year will be (a) half the present year NCERT Page-184 / N-129 (b) one-eighth the present year (c) one-sixth the present year (d) one-tenth the present year 16. A satellite of mass ' m ', moving around the earth in a circular orbit of radius R, has angular momentum L. The areal velocity of satellite is (Me = mass of earth) NCERT Page-185 / N-129 (a) L/2 m (b) L/m (c) 2 L/m (d) 2 L/Me 17. Newton's universal law of gravitation applies to NCERT Page-187 / N-130 (a) small bodies only (b) planets only (c) both small and big bodies (d) only valid for solar system 18. For a particle inside a uniform spherical shell, the gravitational force on the particle is (a) infinite NCERT Page-189 / N-131 (b) zero (c) −Gm1m2 r 2 (d) Gm1m2 r 2 19. Force of gravitational attraction is least NCERT Page-187 / N-130 (a) at the equator (b) at the poles (c) at a point in between equator and any pole (d) None of these 9. 3 UNIVERSAL LAW OF GRAVITATION
20. Two spheres of masses m and M are situated in air and the gravitational force between them is F. The space around the masses is now filled with a liquid of specific gravity 3 . The gravitational force will now be (a) F 9 NCERT Page-187 / N-130 (b) 3F (c) F (d) F 3 21. A mass M is split into two parts m and (M − m), which are then separated by a certain distance. What ratio of m/M maximizes the gravitational force between the two parts? NCERT Page-187 / N-130 (a) 1 3 (b) 1 2 (c) 1 4 (d) 1 5 22. The distance of the centres of moon and earth is D. The mass of earth is 81 times the mass of the moon. At what distance from the centre of the earth, the gravitaional force will be zero? NCERT Page-187 / N-130 (a) D 2 (b) 2D 3 (c) 4D 3 (d) 9D 10 23. Six stars of equal mass are moving about centre of mass of the system such that they are always on the vertices of a regular hexagon of side length a. Their common time period will be NCERT Page-187/N-130 (a) 4π√ a3 Gm (b) 2π√ 4√3a3 Gm(5√3+4) (c) 4π√ 3a3 Gm (d) None of these 24. Two stars of mass m1 and m2 are parts of a binary system. The radii of their orbits are r1 and r2 respectively, measured from the C.M. of the system. The magnitude of gravitational force m1 exerts on m2 is NCERT Page-187 / N-130 (a) m1m2G (r1+r2 )2 (b) m1G (r1+r2 )2 (c) m2G (r1+r2 )2 (d) (m1+m2 ) (r1+r2 )2 25. In the figure, the direction of gravitational force on m1 due to m2 is along NCERT Page-187 / N-130 26. (a) r⃗1 (b) r⃗2 (c) r⃗ (d) −r⃗ 26. Two bodies of masses 4 kg and 9 kg are separated by a distance of 60 cm. A 1 kg mass is placed in between these two masses. If net force on 1 kg is zero, then its distance from 4 kg mass is NCERT Page-187 / N-130 (a) 26 cm (b) 30 cm (c) 28 cm (d) 24 cm