DP Physics (first assessment 2025)

Question EXE.2.SL.TZ0.12

Date	Example questions Example questions	Marks available	[Maximum mark: 7]	Reference code	EXE.2.SL.TZ0.12
Level	SL	Paper	2	Time zone	TZ0
Command term	Determine, Show that	Question number	12	Adapted from	N/A

12.

[Maximum mark: 7]

EXE.2.SL.TZ0.12

One of Kepler’s laws suggests that for moons that have circular orbits around a planet:

$\frac{T^{2}}{4 π r^{3}} = k$

where $T$ is the orbital period of the moon, $r$ is the radius of its circular orbit about the planet, and $k$ is a constant.

(a)

Show that $k = \frac{1}{G M}$ .

[2]

Markscheme

Equates centripetal force (with Newton’s law of gravitation $m r ω^{2} = \frac{G M m}{r^{2}}$ )

$T = \frac{2 π}{ω}$ ✓

Uses both equation correctly with clear re-arrangement ✓

(b)

The table gives data relating to the two moons of Mars.

Determine r for Deimos.

[2]

Markscheme

$r_{De}^{3} = \frac{T_{De}^{2} r_{Ph}^{3}}{T_{Ph}^{2}}$ seen or correct substitution ✓

23.5 Mm ✓

(c)

Determine the mass of Mars.

[3]

Markscheme

Converts T to 27.6 ks and converts to m from Mm ✓

$k = 7.33 \times 10^{- 14}$ «s² m⁻³» ✓

« $M = \frac{1}{k G}$ » $= 2.04 \times 10^{23}$ «kg» ✓

MP1 can be implicit

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