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1. Newton’s law of universal gravitation is mathematically represented as

A. F = G(m₁m₂)/r² B. F = G(m₁ + m₂)/r² C. F = G(m₁ - m₂)/r² D. F = G(m₁m₂)/r

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2. Kepler’s first law states that planets move in

A. Circular orbits B. Elliptical orbits C. Parabolic paths D. Hyperbolic paths

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3. The acceleration due to gravity at a height h above the Earth's surface is given by

A. g(1 + h/R)² B. g(1 - h/R)² C. g/(1 + h/R)² D. g/(1 - h/R)²

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4. The escape velocity from Earth's surface is approximately

A. 7 km/s B. 9.8 km/s C. 11.2 km/s D. 12.5 km/s

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5. Gravitational potential energy at a distance r from a mass M is

A. -GM/r B. -GMm/r C. -GMm/r² D. -Gm/r²

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6. The orbital speed of a satellite in a circular orbit of radius r around Earth is

A. √(GM/r) B. √(GMm/r) C. √(GMr) D. √(Gm/r)

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7. The time period of a satellite orbiting Earth in a circular orbit of radius r is proportional to

A. r B. r³/² C. r² D. r³

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8. The value of gravitational constant G is approximately

A. 6.67 × 10⁻¹¹ N m²/kg² B. 9.8 m/s² C. 3 × 10⁸ m/s D. 1.6 × 10⁻¹⁹ J

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9. If the radius of Earth is reduced to half without changing its mass, the acceleration due to gravity on the surface would become

A. Half B. Double C. Four times D. One-fourth

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10. The gravitational force between two masses is inversely proportional to

A. The distance between them B. The square of the distance between them C. The product of their masses D. The sum of their masses

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11. The work done in moving a mass m from infinity to a point at distance r from a mass M is

A. GMm/r B. -GMm/r C. GMm/r² D. -GMm/r²

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12. The gravitational field intensity at a point inside a uniform spherical shell is

A. Zero B. Constant C. Directly proportional to distance from center D. Inversely proportional to distance from center

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13. The period of revolution of a planet around the sun is proportional to

A. (Semi-major axis)³/² B. (Semi-major axis)²/³ C. (Semi-major axis)² D. (Semi-major axis)³

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14. The gravitational potential at a point on the surface of Earth is

A. -GM/R B. -GM/2R C. -2GM/R D. -GM/4R

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15. The ratio of gravitational force to electrostatic force between two protons is of the order of

A. 10⁻³⁶ B. 10⁻²⁴ C. 10⁻¹⁸ D. 10⁻⁴⁰

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16. The energy required to move a satellite from a lower orbit to a higher orbit

A. Increases B. Decreases C. Remains the same D. Depends on the mass of the satellite only

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17. The gravitational binding energy of a uniform sphere of mass M and radius R is

A. (3/5)GM²/R B. (3/5)GM/R² C. (5/3)GM²/R D. (5/3)GM/R²

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18. The effective value of acceleration due to gravity decreases with

A. Increase in altitude B. Increase in depth C. Increase in latitude D. All of the above

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19. The weight of a body at the center of Earth is

A. Zero B. Equal to its weight on the surface C. Twice its weight on the surface D. Infinite

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20. The gravitational potential energy of a system of two masses m₁ and m₂ separated by a distance r is

A. -Gm₁m₂/r B. Gm₁m₂/r C. -Gm₁m₂/r² D. Gm₁m₂/r²