CIE AS/A Level Physics 13.1 Gravitational field Study Notes- 2025-2027 Syllabus
CIE AS/A Level Physics 12.1 Kinematics of uniform circular motion Study Notes – New Syllabus
CIE AS/A Level Physics 12.1 Kinematics of uniform circular motion Study Notes at IITian Academy focus on specific topic and type of questions asked in actual exam. Study Notes focus on AS/A Level Physics latest syllabus with Candidates should be able to:
- understand that a gravitational field is an example of a field of force and define gravitational field as force per unit mass
- represent a gravitational field by means of field lines
Understanding Gravitational Field as a Field of Force
A gravitational field is a region of space in which a mass experiences a force due to another mass. It is an example of a field of force, meaning that a force acts on objects within the field without the objects being in physical contact.
Definition:
\( \mathrm{Gravitational\ field\ strength,\ g = \dfrac{F}{m}} \)
- \( \mathrm{F} \): force acting on a test mass (N)
- \( \mathrm{m} \): mass of the test object (kg)
- \( \mathrm{g} \): gravitational field strength (N/kg or m/s²)
Interpretation: The gravitational field strength \( \mathrm{g} \) at a point is equal to the force experienced per unit mass placed at that point.
Nature of Gravitational Fields:
- Always attractive, never repulsive.
- Produced by any object with mass.
- Universal — every mass in the universe exerts a gravitational pull on every other mass.
- Acts at a distance — no contact is required between the masses.
Units: Since \( \mathrm{g = F/m} \), its SI unit is \( \mathrm{N/kg} \), which is equivalent to \( \mathrm{m/s^2.} \)
Example
Calculate the gravitational field strength near the surface of Earth if a 2.0 kg object experiences a weight (gravitational force) of 19.6 N.
▶️ Answer / Explanation
Using \( \mathrm{g = \dfrac{F}{m}} \):
\( \mathrm{g = \dfrac{19.6}{2.0} = 9.8 \ N/kg.} \)
Hence, the gravitational field strength near Earth’s surface is \( \mathrm{9.8 \ N/kg.} \)
Interpretation: Every kilogram of mass experiences a downward force of 9.8 N due to Earth’s gravity.
Example
The Moon’s gravitational field strength is \( \mathrm{1.62 \ N/kg.} \) Calculate the weight of an astronaut of mass \( \mathrm{80 \ kg} \) on the Moon and compare it to their weight on Earth (\( \mathrm{g = 9.81 \ N/kg.} \)).
▶️ Answer / Explanation
On Moon:
\( \mathrm{W_{Moon} = mg = 80 \times 1.62 = 130 \ N.} \)
On Earth:
\( \mathrm{W_{Earth} = 80 \times 9.81 = 785 \ N.} \)
Comparison: The astronaut’s weight on the Moon is much smaller (about 1/6th) because the Moon’s gravitational field strength is weaker.
Key Insight: Although the astronaut’s mass remains constant, the gravitational field strength of the celestial body determines the weight experienced.
Representation of Gravitational Fields with Field Lines
A gravitational field can be represented graphically by field lines (also called lines of force). The pattern of these lines shows both the direction and relative strength of the field.
Rules for Drawing Gravitational Field Lines:
- Field lines always point towards the mass producing the field (since gravity is attractive).
- Lines are radial for isolated spherical bodies like Earth.
- The density of field lines indicates field strength — closer lines mean a stronger field.
- Field lines never cross.
Representation for a Spherical Mass:
Uniform Gravitational Field (Near Earth’s Surface):
- Over small regions near Earth’s surface, the field is approximately uniform.
- Field lines are drawn as parallel and equally spaced — direction vertically downward.
Field lines visualize how a gravitational field acts: they point in the direction of the force on a test mass and their spacing shows the field’s relative strength.
Example
Sketch and describe the gravitational field pattern around a single spherical planet.
▶️ Answer / Explanation
- Draw straight lines directed radially inward towards the planet’s centre.
- Lines are closer near the planet (stronger field) and farther apart at larger distances (weaker field).
- All lines terminate at the planet’s centre, showing attraction.
Description: The field is radial and non-uniform — its strength decreases with distance according to \( \mathrm{g \propto \dfrac{1}{r^2}}. \)
Example
Compare and explain the difference between the gravitational field patterns:
- (a) around Earth (radial field)
- (b) near Earth’s surface (uniform field)
▶️ Answer / Explanation
(a) Radial Field (Far from Earth):
- Field lines converge towards Earth’s centre.
- Field strength decreases with distance as \( \mathrm{g = \dfrac{GM}{r^2}}. \)
- Non-uniform field — curved lines pointing inward.
(b) Uniform Field (Near Surface):
- Field lines are parallel and evenly spaced.
- Field strength is nearly constant (\( \mathrm{g = 9.81 \ N/kg.} \))
- Used for practical calculations near Earth’s surface.
Conclusion: A radial field transitions to an approximately uniform field near the planet’s surface because the curvature becomes negligible over small distances compared to Earth’s radius.