Point and spherical masses — OCR A-Level Physics
Test yourself on Point and spherical masses with OCR A-Level practice questions.
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Point and spherical masses explained
Any object with mass produces a gravitational field, a region in which another mass experiences an attractive gravitational force.
Read the full explanation
The field is represented by field lines pointing towards the mass, and its strength at a point is the gravitational force per unit mass on a small test mass placed there. For a point mass or a uniform sphere, the field strength at distance r from the centre is g = GM/r², where G is the gravitational constant and M is the mass producing the field. Doubling the mass doubles the field strength at the same distance; doubling the distance reduces it to one quarter.
(b) modelling the mass of a spherical object as a point mass at its centre
For a uniform sphere, the gravitational field outside the sphere is the same as if all its mass were concentrated at its centre. This point-mass model lets you use g = GM/r² with r measured from the centre, and it also applies to the force between two uniform spheres. The model fails inside the sphere, where the field depends only on the mass enclosed within the radius and falls linearly to zero at the centre for a uniform density. Use the model for satellites, planets and stars when the distance is measured from the centre and the object is treated as spherically symmetric.
(c) gravitational field lines to map gravitational fields
Gravitational field lines are a visual tool to map the gravitational field around a mass. For a point mass or a uniform sphere, the field is radial: lines point towards the centre of the mass, showing the direction of the gravitational force on a small test mass. The spacing of lines indicates field strength: closer lines mean a stronger field. Around a single spherical mass, lines are evenly spaced in angle but their density decreases with distance because field strength follows an inverse-square law. For two masses, the pattern shows attraction, with lines converging on each mass. Field lines never cross, as the field direction is unique at any point. They are used to represent the field without calculations, helping to predict the motion of objects. In an MCQ, you may be asked to identify correct field-line patterns or interpret spacing.
(d) gravitational field strength; g = F/m.
Gravitational field strength g at a point is defined as the gravitational force F per unit mass m placed at that point: g = F/m. It is a vector quantity, directed towards the centre of the mass creating the field. The SI unit is N kg⁻¹, equivalent to m s⁻². For a point mass or uniform sphere of mass M, g = GM/r², where r is the distance from the centre. Near the Earth's surface, g is approximately 9.81 N kg⁻¹. The equation g = F/m allows calculation of the force on a mass in a known field. In an MCQ, you may need to calculate g, F or m, or compare g at different distances.
(e) the concept of gravitational fields as being one of a number of forms of field giving rise to a force.
A field is a region where a force acts on a suitable object. Gravitational fields are one of several types of field, such as electric, magnetic and nuclear fields. Each field gives rise to a force on a property: gravitational fields act on mass, electric fields on charge, magnetic fields on moving charges or magnetic poles. The concept of a field allows forces to be described without contact, explaining action at a distance. Gravitational fields are always attractive and extend infinitely, though their strength decreases with distance. In an MCQ, you may be asked to identify the property affected by each field or compare field types.
Your focus
- State that gravitational fields arise from objects with mass.
- Define gravitational field strength as force per unit mass.
- Apply g = GM/r² to point masses and uniform spheres.
Show all 15 objectives
- Describe the point-mass model for a spherical object.
- Apply g = GM/r² outside a uniform sphere using distance from the centre.
- Recognise the limits of the point-mass model inside a spherical mass.
- Draw and interpret gravitational field lines for a point mass or uniform sphere.
- Explain how the spacing of field lines relates to gravitational field strength.
- Apply the rules of field lines (direction, no crossing) to identify correct diagrams.
- State and use the equation g = F/m to solve problems.
- Describe the direction and units of gravitational field strength.
- Apply g = GM/r² to calculate field strength for a point mass or uniform sphere.
- Describe what a field is and how it gives rise to a force.
- Compare gravitational fields with other types of field.
- Explain how gravitational fields act on mass to produce an attractive force.
Point and spherical masses exam tips
Marking Points
- Mass is the source of a gravitational field; every object with mass has one.
- The gravitational force between two masses is always attractive.
- Gravitational field strength is defined as force per unit mass, g = F/m, measured in N kg⁻¹.
- For a point mass or uniform sphere, g = GM/r² at distance r from the centre.
- Field strength follows an inverse-square dependence on distance from a point mass.
- A uniform spherical mass can be modelled as a point mass located at its centre.
- Outside the sphere, g = GM/r² with r measured from the centre of the sphere.
- The same point-mass model applies to the gravitational force between two uniform spheres.
- Inside a uniform sphere the field is not given by GM/r²; it depends on the mass enclosed within radius r.
- The model requires spherical symmetry and uniform density, or a spherically symmetric mass distribution.
- Field lines point towards the centre of a spherical mass, indicating attraction.
- The direction of the field line at a point gives the direction of the gravitational force on a small test mass placed there.
- The spacing of field lines represents the relative strength of the gravitational field: closer lines indicate a stronger field.
- For a point mass or uniform sphere, the field is radial and the line density decreases with distance from the centre.
- Field lines do not cross because the gravitational field has a unique direction at each point.
- Gravitational field strength g is defined as the gravitational force per unit mass: g = F/m.
- The direction of g is the same as the direction of the gravitational force on a test mass, towards the centre of the attracting mass.
- The SI unit of g is N kg⁻¹, which is equivalent to m s⁻².
- For a point mass or uniform sphere, g = GM/r², showing inverse-square dependence on distance r from the centre.
- The force on a mass m in a gravitational field is F = mg.
- A field is a region where a force is exerted on a suitable object.
- Gravitational fields act on mass and always produce an attractive force.
- Other field types include electric fields (act on charge), magnetic fields (act on moving charges or magnetic poles) and nuclear fields (act on nucleons).
- The concept of a field explains non-contact forces and action at a distance.
- Gravitational field strength decreases with distance from the mass, following an inverse-square law for a point mass.
Examiner Tips
- 💡Quote the definition of gravitational field strength as force per unit mass.
- 💡Use g = GM/r² and substitute distances from the centre of the mass.
- 💡Check units: N kg⁻¹ is equivalent to m s⁻².
- 💡When comparing field strengths, compare the ratio of masses and the inverse ratio of distances squared.
- 💡State that r is the distance from the centre of the sphere.
- 💡Use the point-mass model only for points outside a spherically symmetric mass.
- 💡For inside a uniform sphere, recall that only the enclosed mass contributes to the field.
- 💡When comparing surface and orbital values, substitute the appropriate radius from the centre.
- 💡Remember that gravitational field lines always point towards the mass; use arrows to show direction.
- 💡Use the spacing of lines to compare field strengths: denser lines mean a stronger field.
- 💡Check that lines are radial for a single point mass or uniform sphere and do not cross.
- 💡Use g = F/m to find force, mass or field strength when two quantities are known.
- 💡Remember that g is a vector; include direction when asked.
- 💡Check units: N kg⁻¹ is equivalent to m s⁻².
- 💡Link each field type to the property it acts on: mass for gravitational, charge for electric, moving charge or pole for magnetic.
- 💡Remember that gravitational fields are always attractive and have infinite range.
- 💡Use the field concept to explain non-contact forces.
Common Mistakes
- Believing a gravitational field requires a second mass to exist; the field belongs to the mass that produces it.
- Treating gravitational force as repulsive or as sometimes attractive and sometimes repulsive; it is always attractive.
- Using g = GM/r instead of g = GM/r² for a point mass.
- Forgetting that r is measured from the centre of the spherical mass, not from its surface.
- Measuring r from the surface of a planet rather than from its centre.
- Applying g = GM/r² inside a planet or star where the point-mass model does not hold.
- Assuming the model requires the object to be small; it requires spherical symmetry, not small size.
- Treating a non-spherical body such as a long rod as a point mass at its centre without justification.
- Misunderstanding: field lines point away from a mass. Correction: gravitational field lines point towards the mass because gravity is always attractive.
- Misunderstanding: field lines are equally spaced everywhere around a spherical mass. Correction: spacing increases with distance from the mass, showing that field strength decreases.
- Misunderstanding: field lines can cross. Correction: field lines never cross because that would imply two different force directions at the same point.
- Misunderstanding: field lines represent the path of an object. Correction: they show the direction of the gravitational force at a point, not the trajectory of a moving mass.
- Misunderstanding: g is a force. Correction: g is force per unit mass, a vector field strength, not a force.
- Misunderstanding: g is a scalar. Correction: g has direction (towards the mass) and is a vector.
- Misunderstanding: g is constant everywhere. Correction: g varies with distance from the mass, following an inverse-square law for a point mass or uniform sphere.
- Misunderstanding: g has units of N. Correction: g has units of N kg⁻¹ or m s⁻².
- Misunderstanding: gravitational fields are the only type of field. Correction: there are electric, magnetic and nuclear fields, each acting on different properties.
- Misunderstanding: gravitational fields can be repulsive. Correction: gravitational fields are always attractive.
- Misunderstanding: fields require a medium to act. Correction: fields act through empty space; they do not need a medium.
- Misunderstanding: gravitational field strength is the same everywhere. Correction: it decreases with distance from the mass.