Free NEET Physics multiple-choice questions on Universal Law & g Variations. Attempt each question and reveal the answer with a full explanation.
If the earth stops rotating, the value of 'g' at the equator will: Increase Decrease Remain same Become zero What happens to the gravitational force between two point masses if the space between them is filled with a solid lead block? Remains the same Increases Decreases Becomes zero Two bodies of mass m and 9m are placed at a distance R . The gravitational potential on the line joining the bodies where the gravitational field equals zero, will be ( G = gravitational constant) - 8Gm R - 12Gm R - 16Gm R - 20Gm R The amount of work done to raise a mass ‘ m ’ from the surface of the Earth to a height equal to the radius of the Earth ‘ R ’ will be mg R 2 mgR mg R 4 2 ,mg ,R Two identical lead spheres of radius R are placed in contact with each other. The gravitational force F between them is proportional to: R 4 R 2 R -2 R 6 At what latitude on Earth's surface is the change in the value of g due to Earth's rotation 25 % of its value at the equator? 60 30 45 90 A point mass m is placed at a distance x from the center of a uniform thin rod of length L and mass M on its axial line. The gravitational force on the point mass is: GMm x 2 - (L/2) 2 GMm x 2 GMm x 2 + (L/2) 2 GMm L 2 Two uniform spheres of radius R and 3R are made of the same material. They are placed in contact. The gravitational force between them is proportional to: R 4 R 2 R 3 R 6 A uniform thin rod of mass M and length L is placed on the x-axis. A point mass m is placed at a distance d from one end of the rod. The magnitude of the gravitational force between them is: GMm d(L+d) GMm L 2 GMm d 2 GMm (L+d) 2 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: F F/3 F/9 3F If the distance between the Earth and the Sun were doubled, the gravitational force between them would become: One-fourth Double Half Four times Two planets have the same average density but their radii are R 1 and R 2 . If g 1 and g 2 are the accelerations due to gravity at the surfaces of these planets, then g 1/g 2 is: R 1/R 2 R 2/R 1 R 1 2/R 2 2 (R 1/R 2) 1/2 The Earth is an oblate spheroid. A body is taken from the equator to the North Pole. Its weight will: Increase Decrease Remain same Increase then decrease The change in the value of g at a depth d for d R is approximately proportional to: d d 2 1/d 1/d 2 A body weighs 200 N on the surface of the Earth. How much will it weigh half way down to the center of the Earth? 100 N 150 N 200 N 250 N The height at which the weight of a body becomes 1/16 th its weight on the surface of earth (radius R ) is: 3R 4R 15R 5R Which of the following is responsible for the existence of atmosphere on a planet? v rms < v escape v rms > v escape v rms = v escape Low temperature only If the radius of the Earth were to shrink by 1 % with its mass remaining the same, the acceleration due to gravity on the Earth's surface would: Increase by 2 % Decrease by 2 % Increase by 1 % Decrease by 1 % The height h at which the acceleration due to gravity g h becomes g/n (where g is surface gravity) is given by: R( n - 1) R/n R(n - 1) R n Two stars of masses M and 4M are at a distance d . A particle of mass m is placed on the line joining them such that the net gravitational force on it is zero. The distance of the particle from mass M is: d/3 d/5 d/2 2d/3 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 (distance from the center of Earth remains same) will now be: 9.8 m/s 2 4.9 m/s 2 19.6 m/s 2 39.2 m/s 2 A planet has twice the mass and three times the radius of Earth. The acceleration due to gravity at its surface is g' . The ratio g'/g is: 2/9 2/3 4/9 1/3 The value of the gravitational constant G in the system of units where length is measured in cm, mass in g, and time in s is 6.67 10 -8 . What is its value in SI units? 6.67 10 -11 N m 2 kg -2 6.67 10 -10 N m 2 kg -2 6.67 10 -9 N m 2 kg -2 6.67 10 -12 N m 2 kg -2 If the acceleration due to gravity at a height h is g h and at a depth d is g d , and it is given that g h = g d for h, d R , then the ratio h/d is: 1/2 2 1 1/4 A mass M is split into two parts, m and M-m , which are then separated by a certain distance. What is the ratio m/M so that the gravitational force between them is maximum? 1/2 1/3 1/4 2/3 If a body is taken from the equator to the pole, its weight increases. This is primarily due to: Both the shape of Earth and its rotation Only the rotation of Earth Only the shape of Earth The change in the value of G The height at which the acceleration due to gravity becomes g/9 (where g is the value at the surface) is: 2R 3R R/2 R/3 If the distance between two masses is doubled, the gravitational force between them becomes F . If the masses are also doubled, the new force will be: F 2F 4F F/2 The time period of a simple pendulum inside a satellite orbiting Earth is: Infinite Zero Same as on Earth Depends on the mass of the satellite The gravitational force between two masses is x in vacuum. If both masses are placed in a medium of relative density 3 , the gravitational force will be: x x/3 3x x/9 If the Earth suddenly stops rotating about its axis, the value of g at the equator would: Increase Decrease Remain the same Become zero The acceleration due to gravity on the surface of a planet is g p . If the mass of the planet is M p and its radius is R p , and for Earth the values are g e , M e , and R e , which of the following represents g p/g e ? (M p / M e) (R e / R p) 2 (M p / M e) (R p / R e) 2 (M e / M p) (R p / R e) 2 (M p / M e) (R e / R p) The weight of a body on the surface of Earth is W . If the Earth's radius were to shrink to half its present value without any change in its mass, the weight of the same body on the new surface would be: 4W 2W W/2 W/4 Which of the following graphs best represents the relationship between the gravitational force F between two point masses and the distance r between them? A rectangular hyperbola where F 1/r 2 A straight line passing through origin A parabola A horizontal straight line The weight of an object in the coal mine, sea level, and at the top of the mountain are W 1 , W 2 and W 3 respectively, then: W 1 < W 2 > W 3 W 1 = W 2 = W 3 W 1 > W 2 > W 3 W 1 < W 2 < W 3 Which of the following statements about the gravitational constant G is true? Its value is same throughout the universe Its value depends on the temperature of the masses Its value depends on the medium between the masses Its value depends on the mass of the Earth The force of attraction between two unit masses separated by a unit distance is numerically equal to: Gravitational constant Acceleration due to gravity Gravitational potential Gravitational field At the surface of Earth, the value of g is minimum at: The Equator The Poles The Arctic Circle The Tropic of Cancer A point mass M is divided into two parts xM and (1-x)M . For the gravitational force between them to be maximum for a fixed distance, the value of x should be: 0.5 0.25 0.75 1 If the Earth shrinks such that its density remains constant but its radius decreases to 1/2 of its original value, the acceleration due to gravity on its surface will be: g/2 g/4 2g 4g A planet has a mass four times that of Earth and a radius twice that of Earth. The acceleration due to gravity on its surface is: g 2g 4g g/2 A planet has a radius 1/4 times that of Earth and a mass 1/40 times that of Earth. If g is the acceleration due to gravity on Earth, then the value of g on the planet is: 0.4g 0.1g 1.6g 0.25g If a satellite is at a height h = 0.5R above the Earth's surface, what is the ratio of the acceleration due to gravity at that height to that on the surface? 4/9 2/3 1/2 4/5 The height at which the acceleration due to gravity becomes g/4 is (where R is radius of Earth): R 2R R/2 3R If the distance between two masses is doubled, the gravitational force between them becomes F . If the distance is tripled, the force will be: 4F/9 F/9 F/3 9F/4 Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is g and that on the surface of the new planet is g', then - g'=3g g'=9g g'=g/9 g'=27g The Earth is assumed to be a sphere of radius R. A platform is arranged at a height R from the surface of the Earth. The escape velocity of a body from this platform is fv, where v is its escape velocity from the surface of the Earth. The value of f is:- 2 1 2 1 3 1 2 A body of mass 'm' taken from the earth's surface to the height equal to twice the radius (R) of the earth. The change in potential energy of body will be mg2R 2 3 mgR 3mgR 1 3 mgR If the mass of the Sun were ten times smaller and the universal gravitational constant were ten times larger in magnitude, which of the following is not correct? Time period of a simple pendulum on the Earth would decrease Walking on the ground would become more difficult Raindrops will fall faster 'g' on the Earth will not change A body weighs 200 N on the surface of the earth. How much will it weigh half way down to the centre of the earth ? 100 N 150 N 200 N 250 N A body weighs 72 N on the surface of the earth. What is the gravitational force on it, at a height equal to half the radius of the earth? 32 N 30 N 24 N 48 N Three identical particles, each of mass m , are situated at the vertices of an equilateral triangle of side L . The gravitational field at the centroid of the triangle is: Zero 3Gm/L 2 Gm/L 2 3 Gm/L 2 Right option for the number of tetrahedral and octahedral voids in hexagonal primitive unit cell are : 6, 12 2, 1 12, 6 8, 4 A body of mass 60 g experiences a gravitational force of 3.0 N, when placed at a particular point. The magnitude of the gravitational field intensity at that point is 50 N/kg 20 N/kg 180 N/kg 0.05 N/kg The mass of a planet is 1 10 th that of the earth and its diameter is half that of the earth. The acceleration due to gravity on that planet is: 19.6 m s -2 9.8 m s -2 4.9 m s -2 3.92 m s -2 A body weighs 48 N on the surface of the earth. The gravitational force experienced by the body due to the earth at a height equal to one-third the radius of the earth from its surface is : 36 N 16 N 27 N 32 N The acceleration due to gravity g at a height h above the surface of the Earth is the same as at a depth d below the surface. If h and d are much smaller than the radius of Earth R , then the relation between h and d is: d = 2h d = h d = h/2 d = h 2 Two planets of radii r 1 and r 2 are made from the same material. The ratio of the acceleration due to gravity at their surfaces g 1/g 2 is: r 1/r 2 r 2/r 1 (r 1/r 2) 2 (r 2/r 1) 2 The variation of acceleration due to gravity g with distance r from the center of Earth (radius R ) is best represented by which graph? Linear increase from r=0 to r=R , then hyperbolic decrease Linear increase from r=0 to r=R , then parabolic decrease Constant from r=0 to r=R , then hyperbolic decrease Parabolic increase from r=0 to r=R , then linear decrease Dependence of intensity of gravitational field ( E ) of Earth with distance ( r ) from center of Earth is correctly represented by: Linear increase for r < R , inverse square for r > R Constant for r < R , inverse square for r > R Zero for r < R , inverse square for r > R Inverse square for all r If the mass of the Sun were ten times smaller and the universal gravitational constant G were ten times larger in magnitude, which of the following is not correct? Time period of a simple pendulum on the Earth would decrease Raindrops would fall faster Walking on the ground would become more difficult ' g ' on the Earth would not change If the acceleration due to gravity at a height h above the surface of the Earth is g/9 , then the value of h in terms of Earth's radius R is: 2R R/3 3R R/2 If the acceleration due to gravity on Earth is g , what is the acceleration due to gravity on a planet with twice the radius and twice the density of Earth? 2g g 4g 8g The density of a newly discovered planet is twice that of Earth, and the acceleration due to gravity at its surface is equal to that at the Earth's surface. If the radius of Earth is R , the radius of the planet would be: R/2 2R 4R R/4 What is the fractional decrease in the value of ' g ' at a height of 64 km from the surface of Earth? (Radius of Earth R = 6400 km ) 0.02 0.01 0.25 0.05 At what distance from the center of Earth the value of acceleration due to gravity g is half of its value at the surface? (Radius of Earth is R ) 2 R R/2 2R R/ 2 The ratio of the weight of a body on the Earth's surface to that on the surface of a planet is 9:4. The mass of the planet is 1/9 of that of the Earth. If R is the radius of Earth, what is the radius of the planet? 2R/3 R/2 3R/2 4R/9 At what angular speed should the Earth rotate so that the apparent weight of an object at the equator becomes zero? g/R g/R R/g 2 g/R A body weighs 72 N on the surface of the Earth. What is the gravitational force on it at a height equal to half the radius of the Earth? 32 N 48 N 36 N 18 N If the acceleration due to gravity at the equator is to be zero, the angular velocity of the Earth should be (Take g = 10 m/s 2 and R = 6400 km ): 1.25 10 -3 rad/s 1.5 10 -3 rad/s 0.5 10 -3 rad/s 1.25 10 -2 rad/s Two stars of masses m and 2m are parts of a binary star system with their centers separated by distance d . The ratio of their orbital radii r 1/r 2 about their common center of mass is: 2:1 1:2 4:1 1:4 A satellite moves in a circular orbit around the Earth. The radius of the orbit is twice the radius of the Earth. The acceleration due to gravity experienced by the satellite is: 2.45 m/s 2 4.9 m/s 2 9.8 m/s 2 1.22 m/s 2 A simple pendulum has a time period T 1 when on the earth's surface and T 2 when taken to a height R above the earth's surface ( R is radius of earth). The ratio T 2/T 1 is: 2 4 2 1/2 Three particles, each of mass m , are situated at the vertices of an equilateral triangle of side length a . The magnitude of the gravitational force exerted by this system on another particle of mass m kept at the centroid of the triangle is: Zero 3Gm 2 a 2 3 3 Gm 2 a 2 Gm 2 a 2 Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is g and that on the surface of the new planet is g' , then: g' = 3g g' = 9g g' = g/3 g' = 27g If the earth rotates faster than its present speed, the weight of an object will: Decrease at the equator but remain unchanged at the poles Increase at the equator but remain unchanged at the poles Decrease everywhere Remain unchanged everywhere If the Earth were to rotate at such an angular speed that the weight of a body at the equator becomes zero, what would be the approximate duration of the day in minutes? 84 minutes 60 minutes 120 minutes 42 minutes If a body is dropped from a height h = 3R from the Earth's surface, its velocity when it hits the surface is ( g is acceleration due to gravity at surface): 1.5 gR 2 gR 3 gR 0.5 gR If the distance between the Earth and the Moon is r and the mass of Earth is 81 times that of the Moon, at what distance from the Earth's center will the net gravitational field be zero? 0.9 r 0.8 r 0.5 r 0.1 r At what latitude is the effective acceleration due to gravity g' equal to g - 1 4 R 2 , where is the angular velocity of Earth? 60 30 45 0 Which of the following graphs best represents the variation of gravitational field intensity E with distance r from the center of a thin spherical shell of radius R ? E=0 for r < R , then E 1/r 2 for r > R Linear increase for r < R , then 1/r 2 for r > R E 1/r 2 for all r Constant E for r < R , then E=0 for r > R A planet has a mass 8 times that of Earth and a density equal to that of Earth. The acceleration due to gravity at the surface of the planet is g' . The ratio g'/g is: 2 4 8 2 The distance between the centers of the Earth and the Moon is D . The mass of the Earth is 81 times the mass of the Moon. At what distance from the center of the Earth is the gravitational field zero? 0.9 D 0.1 D 0.5 D 0.81 D The gravitational force between two objects of mass m 1 and m 2 separated by distance r is F . If a third mass m 3 is placed near them, the gravitational force between m 1 and m 2 will: remain F increase decrease depend on the value of m 3 If the radius of the Earth is R and the acceleration due to gravity at its surface is g , the value of the acceleration due to gravity at a height h = 3R above the surface is: g/16 g/9 g/4 g/3 The value of g at a depth d below the surface of Earth is g d = g(1 - d/R) . This formula is valid for: All values of d R Only for d R Only for d > R Only at the center If the acceleration due to gravity at a height h is 1 % less than its value at the surface, then h is approximately (given R = 6400 km ): 32 km 64 km 128 km 16 km If the density of a planet is constant, then the variation of the acceleration due to gravity g on its surface with its radius R is: g R g 1/R g R 2 g 1/R 2 At what height above the Earth's surface does the acceleration due to gravity become 1 % of its value at the Earth's surface? ( R is the radius of Earth) 9R 10R 8R 99R If the acceleration due to gravity g at the surface of Earth is 9.8 m/s 2 , what is the value of g at a latitude of 60 ? (Assume Earth is a perfect sphere of radius R = 6400 km and is its angular velocity) g - 1 4 R 2 g - 3 4 R 2 g - 1 2 R 2 g - R 2 Two bodies of mass 10 kg and 1000 kg are at a distance 1 m apart. At which point on the line joining them will the gravitational field be zero? 1 11 m from 10 kg mass 1 10 m from 10 kg mass 1 9 m from 10 kg mass 10 11 m from 10 kg mass The change in the value of acceleration due to gravity g at a latitude of 30 from the equator due to the rotation of the Earth is (where R is the radius of Earth and is its angular velocity): 3 4 R 2 1 4 R 2 1 2 R 2 3 2 R 2 If the Earth were to rotate with an angular velocity such that a body at the equator would feel weightless, the duration of the day would be approximately: 84.6 minutes 24 hours 1.4 hours 42 minutes The ratio of acceleration due to gravity at a depth R/2 to that at a height R/2 from the Earth's surface is: 9/8 8/9 2/3 1/1 A body is dropped from a height h = R (where R is the radius of the Earth) above the Earth's surface. The speed with which it hits the Earth's surface is (neglecting air resistance, g is acceleration due to gravity on the surface): gR 2gR gR/2 2 gR The weight of a body on the Earth's surface is W . At a height h = 2R from the surface, its weight would be: W/9 W/4 W/3 W/16 At a latitude of 60 , the effective acceleration due to gravity g' due to the rotation of the Earth is (where g is the value without rotation): g - 1 4 R 2 g - 3 4 R 2 g - R 2 g - 1 2 R 2 The average density of the Earth can be expressed in terms of g, G and R as: = 3g 4 GR = 4 g 3GR = 3GR 4 g = 4 GR 3g Assuming the sun to have a spherical outer surface of radius r, radiating like a black body at temperature t°C, the power received by a unit surface, (normal to the incident rays) at a distance R from the centre of the sun is r 2 (t + 273) 4 4 R 2 16 2 r 2 t 4 R 2 r 2 (t + 273) 4 R 2 4 r 2 t 4 R 2 Infinite number of bodies, each of mass 2 kg are situated on x-axis at distance 1 m, 2 m, 4 m, 8 m, ..... respectively, from the origin. The resulting gravitational potential due to this system at the origin will be -G - 8 3 G - 4 3 G -4G A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would earth (mass = 5.98 10 24 kg) have to be compressed to be a black hole ? 10 -9 m 10 -6 m 10 -2 m 100 m Dependence of intensity of gravitational field (E) of earth with distance (r) from centre of earth is correctly represented by :- At what height from the surface of earth the gravitation potential and the value of g are -5.4 10 7 J kg -2 and 6.0 ms -2 respectively ? Take the radius of earth as 6400 km : 2600 km 1600 km 1400 km 2000 km The ratio of escape velocity at earth ( v e ) to the escape velocity at a planet ( v p ) whose radius and mean density are twice as that of earth is :- 1 : 2 1 : 2 2 1 : 4 1 : 2 Imagine earth to be a solid sphere of mass M and radius R. If the value of acceleration due to gravity at a depth ‘d’ below earth’s surface is same as its value at a height ‘h’ above its surface and equal to g 4 (where g is the value of acceleration due to gravity on the surface of earth), the ratio of h d will be : 1 4 3 3 2 2 3 The work done to raise a mass m from the surface of the earth to a height h, which is equal to the radius of the earth, is: 3 2 mgR mgR 2mgR 1 2 mgR