6.2 Gravitation

Which of the following best describes Newton's Universal Law of Gravitation?

A. Every object in the universe attracts every other object with a force that is directly proportional to the product of their masses.

B. Every object in the universe repels every other object with a force that is inversely proportional to the square of the distance between their centres.

C. The gravitational force between two objects is directly proportional to the square of the distance between their centres.

D. The gravitational force between two objects is always attractive and its magnitude decreases with increasing mass.

What is the direction of the gravitational field due to a point mass?

A. Tangential to the point mass

B. Away from the point mass

C. Towards the point mass

D. Perpendicular to the point mass

Which of the following best describes the gravitational potential energy of an object at a height h above the Earth's surface?

A. It is zero when h is zero.

B. It is maximum when h is zero.

C. It is negative and becomes less negative as h increases.

D. It is positive and decreases as h increases.

Which of Kepler's laws states that the square of the period of revolution of a planet is directly proportional to the cube of its average distance from the Sun?

A. First law

B. Second law

C. Third law

D. None of the above

A satellite in which type of orbit appears stationary relative to a point on the Earth's equator?

A. Polar orbit

B. Geosynchronous orbit

C. Geostationary orbit

D. Elliptical orbit

a) Define Newton's universal law of gravitation and state its significance in understanding the motion of celestial bodies. [3]

b) Two identical spheres, each of mass 5 kg, are placed 0.5 m apart (centre to centre). Calculate the gravitational force between them using the universal gravitational constant G = 6.67 x 10^-11 Nm^2/kg^2. [2]

a) Describe the concept of gravitational field strength and how it varies with distance from a massive object. [3]

b) Calculate the gravitational field strength on the surface of a planet with a radius of 4000 km and a mass of 5 x 10^24 kg. [2]

a) Explain the concept of gravitational potential energy and how it is affected by the position of an object in a gravitational field. [3]

b) A satellite of mass 1000 kg is placed 8000 km above the Earth's surface. Calculate its gravitational potential energy relative to infinity. Use Earth's mass M = 6 x 10^24 kg and radius R = 6400 km. [2]

a) Explain the inverse-square nature of Newton's universal law of gravitation. [2]

b) A planet has half the radius of Earth but the same mass. How would the gravitational force on the surface of this planet compare to that on Earth? [2]

c) If the acceleration due to gravity on the surface of Earth is 9.8 m/s^2, calculate the acceleration due to gravity on the surface of this planet. [3]

a) Describe the concept of a gravitational field and its direction. [2]

b) How does the gravitational field strength vary as one moves away from the centre of a massive object? [2]

c) Calculate the gravitational field strength 10,000 km above the Earth's surface. Use Earth's radius R = 6400 km and gravitational acceleration g = 9.8 m/s^2. [3]