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Date November 2016 Marks available 2 Reference code 16N.2.SL.TZ0.6
Level Standard level Paper Paper 2 Time zone 0 - no time zone
Command term Define and State Question number 6 Adapted from N/A

Question

(i) Define gravitational field strength.

(ii) State the SI unit for gravitational field strength.

[2]
a.

A planet orbits the Sun in a circular orbit with orbital period T and orbital radius R. The mass of the Sun is M.

(i) Show that T = 4 π 2 R 3 G M .

(ii) The Earth’s orbit around the Sun is almost circular with radius 1.5×1011 m. Estimate the mass of the Sun.

[4]
b.

Markscheme

(i)  «gravitational» force per unit mass on a «small or test» mass 

 

(ii)  N kg–1

Award mark if N kg-1 is seen, treating any further work as neutral.
Do not accept bald m s–2

a.

i
clear evidence that v in  v 2 = 4 π 2 R 2 T 2 is equated to orbital speed  G M R
OR
clear evidence that centripetal force is equated to gravitational force
OR
clear evidence that a in  a = v 2 R etc is equated to g in  g = G M R 2 with consistent use of symbols
Minimum is a statement that G M R is the orbital speed which is then used in v = 2 π R T
Minimum is Fc = Fg ignore any signs.
Minimum is g = a.

substitutes and re-arranges to obtain result
Allow any legitimate method not identified here.
Do not allow spurious methods involving equations of shm etc

T = 4 π 2 R ( G M R 2 ) = 4 π 2 R 3 G M

ii
«= 365 × 24 × 60 × 60 = 3.15 × 10

M = 4 π 2 R 3 G T 2 =≫ = 4 × 3.14 2 × ( 1.5 × 10 11 ) 3 6.67 × 10 11 × ( 3.15 × 10 7 ) 2
2×1030«kg»

Allow use of 3.16 x 107 s for year length (quoted elsewhere in paper).
Condone error in power of ten in MP1.
Award [1 max] if incorrect time used (24 h is sometimes seen, leading to 2.66 x 1035 kg).
Units are not required, but if not given assume kg and mark POT accordingly if power wrong.
Award [2] for a bald correct answer.
No sf penalty here.

b.

Examiners report

[N/A]
a.
[N/A]
b.

Syllabus sections

Core » Topic 6: Circular motion and gravitation » 6.2 – Newton’s law of gravitation
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Core » Topic 6: Circular motion and gravitation
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