AQA A-Level Physics: Gravitational Field Lines and Gravitational Field Strength — mark scheme explained

The question

Calculate the gravitational field strength at a distance of 4,000 km from the center of a planet with a mass of 7 × 10 23 kg. [Paraphrased for study — not reproduced from any exam paper.]

Mark scheme, decoded

What each mark is really for — in plain English — and the wording trap that loses it.

• S1

  Identify the given values: M = 7 × 10 23 kg, r = 4,000 km = 4,000,000 m, and G = 6.674 × 10 -11 N·m 2 /kg 2 .

• S2

  Use the formula for gravitational field strength in a radial field: g = GM r 2

• S3

  Substitute the values into the formula: g = (6.674 × 10 -11 ) (7 × 10 23 ) (4,000,000) 2

• S4

  Calculate the numerator: (6.674 × 10 -11 ) (7 × 10 23 ) = 4.6718 × 10 13 N·m 2 /kg

• S5

  Calculate the denominator: (4,000,000) 2 = 1.6 × 10 13 m 2

• S6

  Divide the numerator by the denominator: g ≈ 4.6718 × 10 13 1.6 × 10 13

• S7

  Simplify the result: g ≈ 2.92 m/s 2

Model answer

Worked through, with each step tagged to the mark it earns.

1. S1

   Identify the given values: M = 7 × 10 23 kg, r = 4,000 km = 4,000,000 m, and G = 6.674 × 10 -11 N·m 2 /kg 2 .

2. S2

   Use the formula for gravitational field strength in a radial field: g = GM r 2

3. S3

   Substitute the values into the formula: g = (6.674 × 10 -11 ) (7 × 10 23 ) (4,000,000) 2

4. S4

   Calculate the numerator: (6.674 × 10 -11 ) (7 × 10 23 ) = 4.6718 × 10 13 N·m 2 /kg

5. S5

   Calculate the denominator: (4,000,000) 2 = 1.6 × 10 13 m 2

6. S6

   Divide the numerator by the denominator: g ≈ 4.6718 × 10 13 1.6 × 10 13

7. S7

   Simplify the result: g ≈ 2.92 m/s 2

8. Final answer: 2.92 m/s 2

Common mistakes

• Confusing the units of gravitational field strength — Always remember that the unit of gravitational field strength is newtons per kilogram (N/kg) or meters per second squared (m/s 2 ).
• Using the wrong formula for gravitational field strength — Ensure you are using the correct formula: g = GM r 2 . The gravitational force formula is F = Gm 1 m 2 r 2 .
• Forgetting to convert distances from kilometers to meters — Always ensure that all distances are in meters before substituting them into the formula. For example, 10,000 km = 10,000,000 m.
• Misinterpreting the direction of gravitational field lines — Gravitational field lines always point towards the mass, indicating the attractive nature of gravity. This is different from electric field lines, which can point away from positive charges.
• Using the wrong value for the gravitational constant — Always use the correct value of the gravitational constant: G = 6.674 × 10 -11 N·m 2 /kg 2 . Double-check that you have included it in your calculations.
• Confusing the radius of a planet with the distance from its center — When calculating gravitational field strength at a point outside the surface of a planet, add the altitude to the radius of the planet to get the total distance r from the center. For example, if you are 1,000 km above the surface of a planet with a radius of 5,000 km, r = 6,000 km.

Where the marks go

• Full worked solution (all marking points)6 marks

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