Tiêu đề 8.GRAVITATION - Questions.pdf ✅

8.GRAVITATION (1.)According to Kepler’s law T 2 is proportional to (a.) R 3 (b.) R 2 (c.) R (d.) R −1 (2.)A spherical planet for out in space has a mass M0 and diameter D0. A particle of mass m falling freely new the surface of this planet will experience an acceleration due to gravity which is equal to (a.) GM0/D0 2 (b.) 4mGM0/D0 2 (c.) 4GM0/D0 2 (d.) GmM0/D0 2 (3.)The time period T of the moon of planet Mars (mass Mm) is related to its orbital radius R(G = Gravitational constant) as (a.) T 2 = 4π 2R 3 GMm (b.) T 2 = 4π 2GR3 Mm (c.) T 2 = 2πR 3G Mm (d.) T 2 = 4πMmGR 3 (4.)In the following four periods (i) Time of revolution of a satellite just above the earth’s surface (Tst) (ii) Period of oscillation of mass inside the tunnel bored along the diameter of the earth (Tma) (iii) Period of simple pendulum having a length equal to the earth’s radius in a uniform field of 9.8N/kg(Tsp) (iv) Period of an infinite length simple pendulum in the earth’s real gravitational filed (Tis) (a.) Tst > Tma (b.) Tma > Tst (c.) Tsp > Tis (d.) Tst = Tma = Tsp = Tis (5.)If a planet of given density were made larger (keeping its density unchanged) its force of attraction for an object on its surface would increase because of increased mass of the planet but would decrease because of larger separation between the centre of the planet and its surface. Which effect would dominate? (a.) Increase in mass (b.) Increase in radius (c.) Both affect the attraction equally (d.) None of the above (6.)The weight of a body on surface of earth is 12.6 N. When it is raised to a height half the radius of earth its weight will be (a.) 2.8 N (b.) 5.6 N (c.) 12.5 N (d.) 25. 2N (7.)If r denotes the distance between the sun and the earth, then the angular momentum of the earth around the sun is proportional to (a.) r 3/2 (b.) r (c.) √r (d.) r 2 (8.)If the radius of the earth shrinks by 1%, its mass remaining same, the acceleration due to gravity on the surface of earth will (a.) Decrease by 2% (b.) Decrease by 0.5% (c.) Increase by 2% (d.) Increase by 0.5% (9.)An asteroid of mass m is approaching earth, initially at a distance of 10 Re with speed vi . It hits the earth with a speed vf (Re and Me are radius and mass of earth), then (a.) vf 2 = vi 2 + 2Gm MeR (1 − 1 10) (b.) vf 2 = vi 2 + 2GMe Re (1 + 1 10) (c.) vf 2 = vi 2 + 2GMe Re (1 − 1 10) (d.) vf 2 = vi 2 + 2Gm Re (1 − 1 10) (10.)Assuming that the earth is a sphere of radius RE with uniform density, the distance from its centre at which the acceleration due to gravity is equal to g 3 (g is the acceleration due to gravity on the surface of earth) is (a.) RE 3 (b.) 2RE 3 (c.) RE 2 (d.) RE 4 (11.)Where can a geostationary satellite be installed (a.) Over any city on the equator (b.) Over the north or south pole (c.) At height R above earth (d.) At the surface of earth (12.)If density of earth increased 4 times and its radius become half of what it is, our weight will (a.) Be four times its present value (b.) Be doubled (c.) Remain same (d.) Be halved
(13.)LANDSAT series of satellites move in near polar orbits at an altitude of (a.) 3600 km (b.) 3000 km (c.) 918 km (d.) 512 km (14.)If suddenly the gravitational force of attraction between earth and a satellite revolving around it becomes zero, then the satellite will (a.) Continue to move in its orbit with same velocity (b.) Move tangentially to the original orbit with the same velocity (c.) Become stationary in its orbit (d.) Move towards the earth (15.)The largest and the shortest distance of the earth from the sun are r1 and r2, its distance from the sun when it is at the perpendicular to the major axis of the orbit drawn from the sun (a.) r1+r2 4 (b.) r1r2 r1+r2 (c.) 2r1r2 r1+r2 (d.) r1+r2 3 (16.)The ratio of acceleration due to gravity at a height 3R above earth’s surface to the acceleration due to gravity on the surface of the earth is (R = radius of earth) (a.) 1 9 (b.) 1 4 (c.) 1 16 (d.) 1 3 (17.)What is the height the weight of body will be the same as at the same depth from the surface of the earth? Radius of earth is R (a.) R 2 (b.) √5R − R (c.) √5R−R 2 (d.) √3R−R 2 (18.)The time period of an earth satellite in circular orbit is independent of (a.) The mass of the satellite (b.) Radius of its orbit (c.) Both the mass and radius of the orbit (d.) Neither the mass of the satellite nor the radius of its orbit (19.)If the distance between two masses is doubled, the gravitational attraction between them (a.) Is doubled (b.) Becomes four times (c.) Is reduced to half (d.) Is reduced to a quarter (20.)If the force inside the earth surface varies as x n , where r is the distance of body from the centre of earth, then the value of n will be (a.) −1 (b.) −2 (c.) 1 (d.) 2 (21.)A body of weight 500 N on the surface of the earth. How much would it weigh half-way below the surface of the earth? (a.) 125 N (b.) 250 N (c.) 500 N (d.) 1000 N (22.)Three identical bodies of mass M are located at the vertices of an equilateral triangle of side L. They revolve under the effect of mutual gravitational force in a circular orbit, circumscribing the triangle while preserving the equilateral triangle. Their orbital velocity is (a.) √ GM L (b.) √ 3GM 2L (c.) √ 3GM L (d.) √ 2GM 3L (23.)The moon’s radius is 1/4 that of the earth and its mass is 1/80 times that of the earth. If g represents the acceleration due to gravity on the surface of the earth, that on the surface of the moon is (a.) g/4 (b.) g/5 (c.) g/6 (d.) g/8 (24.)A body is taken to a height of nR from the surface of the earth. The ratio of the acceleration due to gravity on the surface to that at the altitude is (a.) (n + 1) 2 (b.) (n + 1) −2 (c.) (n + 1) −1 (d.) (n + 1) (25.)A geostationary satellite is revolving around the earth. To make it escape from gravitational field of earth, its velocity must be increased (a.) 100% (b.) 41.4% (c.) 50% (d.) 59.6%
(26.)The radius of the earth is about 6400 km and that of the mars is 3200 km. The mass of the earth is about 10 times the mass of the mars. An object weighs 200 N on the surface of earth, its weight on the surface of mars will be (a.) 8 N (b.) 20 N (c.) 40 N (d.) 80 N (27.)If the density of a small planet is the same as that of earth, while the radius of the planet is 0.2 times that of the earth, the gravitational acceleration of the surface of that planet is (a.) 0.2 g (b.) 0.4 g (c.) 2 g (d.) 4 g (28.)If g is the acceleration due to gravity on the surface of earth, its value at a height equal to double the radius of earth is (a.) g (b.) g 2 (c.) g 3 (d.) g 9 (29.)Two identical thin rings each of radius R are coaxially placed at a distance R. If the rings have a uniform mass distribution and each has mass m1 and m2 respectively, then the work done in moving a mass m from centre of one ring to that of the other is (a.) Gmm1(√2+1) m2R (b.) Gm(m1−m2)(√2+1) √2R (c.) Gm√2(m1+m2) R (d.) Zero (30.)An astronaut orbiting the earth in a circular orbit 120 km above the surface of earth, gently drops a spoon out of space-ship. The spoon will (a.) Fall vertically down to the earth (b.) Move towards the moon (c.) Will move along with space-ship (d.) Will move in an irregular way then fall down to earth (31.)The earth (mass = 6 × 1024kg) revolves around the sun with angular velocity 2 × 10−7 rads −1 in a circular orbit of radius 1.5 × 108km. The force exerted by the sun on the earth in newton is (a.) Zero (b.) 18 × 1025 (c.) 27 × 1039 (d.) 36 × 1021 (32.)The value of ′g′ at a particular point is 9.8 m/s 2 . Suppose the earth suddenly shrinks uniformly to half its present size without losing any mass. The value of ′g′ at the same point (assuming that the distance of the point from the centre of earth does not shrink) will now be (a.) 4.9 m/sec2 (b.) 3.1 m/sec2 (c.) 9.8 m/sec2 (d.) 19.6 m/sec2 (33.)At what height in km over the earth’s pole the free fall acceleration decreases by one percent? (Assume the radius of the earth to be 6400 km) (a.) 32 (b.) 64 (c.) 80 (d.) 1.253 (34.)The radius of a planet is 1/4 of earth’s radius and its acceleration due to gravity is double that of earth’s acceleration due to gravity. How many times will the escape velocity at the planet’s surface be as compared to its value on earth’s surface (a.) 1 √2 (b.) √2 (c.) 2√2 (d.) 2 (35.)As we go from the equator to the poles, the value of g (a.) Remains the same (b.) Decreases (c.) Increases (d.) Decreases upto a latitude of 45° (36.)Weight of a body of mass m decreases by 1% when it is raised to height h above the earth’s surface. If the body is taken on a depth h in a mine, change in its weight is (a.) 0.5% decrease (b.) 2% decrease (c.) 0.5% increase (d.) 1% increase (37.)If the earth were to spin faster, acceleration due to gravity at the poles (a.) increase (b.) decreases (c.) remain the same (d.) depends on how fast it spins
(38.)Two identical satellites are at R and 7R away from earth surface, the wrong statement is (R =Radius of earth) (a.) Ratio of total energy will be y (b.) Ratio of kinetic energies will be y (c.) Ratio of potential energies will be y (d.) Ratio of total energy will be y but ratio of potential and kinetic energy will be z (39.)Sun is about 330 times heavier and 100 times bigger in radius than earth. The ratio of mean density of the sun to that of earth is (a.) 3.3 × 10−6 (b.) 3.3 × 10−4 (c.) 3.3 × 10−2 (d.) 1.3 (40.)Kepler discovered (a.) Laws of motion (b.) Laws of rotational motion (c.) Laws of planetary motion (d.) Laws of curvilinear motion (41.)If acceleration due to gravity on the surface of a planet is two times that on surface of earth and its radius is double that of earth. Then escape velocity from the surface of that planet in comparison to earth will be (a.) 2 ve (b.) 3 ve (c.) 4 ve (d.) None of these (42.)What is the binding energy of earth-sun system neglecting the effect of other planets and satellites? (Mass of earth Me = 6 × 1024kg, mass of the sun Mx = 2 × 1030kg −2 ) (a.) 8.8 × 1010 J (b.) 8.8 × 103 J (c.) 5.2 × 1033 J (d.) 2.6 × 1033 J (43.)Two equal masses m and m are hung from a balance whose scale pans differ in height by h. If ρ is the mean density of earth, then the error in weighing is (a.) Zero (b.) 4πGρmh/3 (c.) 8πGρmh/3 (d.) 2πGρmh/3 (44.)The additional kinetic energy to be provided to a satellite of mass m revolving around a planet of mass M, to transfer it from a circular orbit of radius R1 to another of radius R2(R2 > R1) is (a.) GmM ( 1 R1 2 − 1 R2 2) (b.) GmM ( 1 R1 − 1 R2 ) (c.) 2GmM ( 1 R1 − 1 R2 ) (d.) 1 2 GmM ( 1 R1 − 1 R2 ) (45.)P is point at a distance r from the centre of a solid sphere of radius r. The variation of gravitational potential at P (ie, V) and distance r from the centre of sphere is represented by the curve. (a.) (b.) (c.) (d.) (46.)For a body lying on the equator to appear weightless, what should be the angular speed of the earth?(Take g = 10ms −2 ; radius of earth = 6400 km) (a.) 0.125 rads −1 (b. ) 1.25 rads −1 (c.) 1.25 × 10−3 rads −1 (d. ) 1.25 × 10−2 rads −1 (47.)One can easily “weight the earth” by calculating the mass of earth using the formula (in usual notation) (a.) G g RE 2 (b.) g G RE 2 (c.) g G RE (d.) G g RE 3 (48.)Gravitational potential on the surface of earth is (M =mass of the earth, R = radius of earth) (a.) −GM/2R (b.) −gR (c.) gR (d.) GM/R (49.)A spaceship is launched into a circular orbit close to earth’s surface. The additional velocity that should be imparted to the spaceship in the orbit to overcome the gravitational pull is (Radius of earth = 6400 km and g = 9.8 ms −2 ) (a.) 11.2 kms −1 (b. ) 8 kms −1 (c.) 3.2 kms −1