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.

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]

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) 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]

Which of the following is NOT a consequence of Kepler's Second Law?

A. Planets move faster in their orbits when they are closer to the Sun.

B. The area swept out by the line joining a planet to the Sun is constant over equal intervals of time.

C. Planets have elliptical orbits with the Sun at one of the foci.

D. The gravitational force between a planet and the Sun is always directed towards the centre of the Sun.

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]

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.

The gravitational force between two objects is F when they are separated by a distance d. If the distance between them is halved, what will be the new gravitational force?

A. F

B. 2F

C. 4F

D. F/4

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 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

What is the escape velocity from the Earth's surface?

A. The minimum velocity required to break free from the Earth's gravitational pull without any further propulsion.

B. The maximum velocity required to remain in orbit around the Earth.

C. The velocity required to reach the Moon.

D. The velocity required to reach the nearest star.

If the mass of the Earth were to double while its radius remains the same, what would happen to the weight of an object on its surface?

A. It would remain the same.

B. It would double.

C. It would halve.

D. It would quadruple.

Which of the following best describes the gravitational field strength at a point in space?

A. It is the force experienced by a unit positive charge placed at that point.

B. It is the force experienced by a unit mass placed at that point.

C. It is the work done in moving a unit positive charge from infinity to that point.

D. It is the potential energy of a unit mass placed at that point.

a) What is meant by escape velocity? [2]

b) Describe the factors on which escape velocity depends. [2]

c) Calculate the escape velocity for a planet with twice the mass of Earth and the same radius. Use Earth's escape velocity v = 11.2 km/s and gravitational constant G = 6.67 x 10^-11 Nm^2/kg^2. [3]

a) State Kepler's second law of planetary motion. [2]

b) Explain the significance of this law in understanding the motion of planets around the Sun. [3]

c) A planet is observed to sweep out equal areas in equal intervals of time. What can be inferred about the planet's speed as it moves closer to and farther from the Sun? [2]

a) Define the term 'gravitational constant' and provide its value. [2]

b) How does the gravitational force between two objects change if the distance between them is halved? [2]

c) A satellite orbits Earth at a height where the gravitational force acting on it is one-fourth of its weight on the surface. Calculate the altitude of the satellite from the Earth's surface. Use Earth's radius R = 6400 km. [3]

d) What would be the effect on the satellite's orbital period if its altitude is doubled? [3]

a) Describe the concept of 'gravitational potential energy'. [2]

b) How does the gravitational potential energy of an object change as it moves farther away from the centre of a massive body? [2]

c) Calculate the change in gravitational potential energy when a 10 kg object is raised to a height of 100 m above the Earth's surface. Use g = 9.8 m/s^2. [3]

d) If the object is then allowed to fall freely, what will be its speed just before it hits the ground? [3]

a) Differentiate between geostationary and geosynchronous orbits. [3]

b) Why are geostationary satellites typically positioned over the equator? [2]

c) Calculate the altitude at which a satellite must orbit Earth to be in a geostationary orbit. Use Earth's radius R = 6400 km and gravitational acceleration g = 9.8 m/s^2. [4]

d) What are the implications for a satellite if it is slightly off from a geostationary orbit? [3]