OCR · A-Level · Physics
Course version: H556 · Version from Sept 2015
(b) modelling the mass of a spherical object as a point mass at its centre
Full specification wording
Point and spherical masses: (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.
Checked against the OCR H556 specification (opens in a new tab) on .
- Point 2 of 5
- 2 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
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.
What earns the marks
- 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.
Common mistakes and how to put them right
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.
Put it right: 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.
Exam tips
- 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.
Try the lesson
The start of the Point and spherical masses: (b) modelling the mass of a spherical object as a point mass at its centre lesson, made from checked teaching notes for this specification point.
Listen
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. A strong answer earns marks for these points. 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. Exam tip: State that r is the distance from the centre of the sphere.
Key words
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Point-mass model
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Gravitational field outside and inside a sphere
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See every definition
- Point-mass model
- A uniform spherical mass can be modelled as a point mass located at its centre.
- Gravitational field outside and inside a sphere
- Outside the sphere, g = GM/r² with r measured from the centre; inside a uniform sphere the field is not given by GM/r² and depends on the mass enclosed within radius r.
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