DP Physics (first assessment 2025)

Question 21M.2.HL.TZ2.10

Date	May 2021	Marks available	[Maximum mark: 7]	Reference code	21M.2.HL.TZ2.10
Level	HL	Paper	2	Time zone	TZ2
Command term	Calculate, Outline, Show that	Question number	10	Adapted from	N/A

10.

[Maximum mark: 7]

21M.2.HL.TZ2.10

The table gives data for Jupiter and three of its moons, including the radius r of each object.

A spacecraft is to be sent from $Io$ to infinity.

(a)

Calculate, for the surface of $Io$ , the gravitational field strength g_Io due to the mass of $Io$ . State an appropriate unit for your answer.

[2]

Markscheme

$« \frac{G M}{r^{2}} = \frac{6.67 \times 10^{- 11} \times 8.9 \times 10^{22}}{{(1.8 \times 10^{6})}^{2}} = » 1.8$ ✓

N kg⁻¹OR m s⁻² ✓

(b.i)

Show that the $\frac{gravitational potential due to Jupiter at the orbit of Io}{gravitational potential due to Io at the surface of Io}$ is about 80.

[2]

Markscheme

$\frac{1.9 \times 10^{27}}{4.9 \times 10^{8}}$ AND $\frac{8.9 \times 10^{22}}{1.8 \times 10^{6}}$ seen ✓

$« \frac{1.9 \times 10^{27} \times 1.8 \times 10^{6}}{4.9 \times 10^{8} \times 8.9 \times 10^{22}} = » 78$ ✓

For MP1, potentials can be seen individually or as a ratio.

(b.ii)

Outline, using (b)(i), why it is not correct to use the equation $\sqrt{\frac{2 G \times mass of Io}{radius of Io}}$ to calculate the speed required for the spacecraft to reach infinity from the surface of $Io$ .

[1]

Markscheme

«this is the escape speed for $Io$ alone but» gravitational potential / field of Jupiter must be taken into account ✓

OWTTE

(c)

An engineer needs to move a space probe of mass 3600 kg from Ganymede to Callisto. Calculate the energy required to move the probe from the orbital radius of Ganymede to the orbital radius of Callisto. Ignore the mass of the moons in your calculation.

[2]

Markscheme

$- G M_{Jupiter} (\frac{1}{1.88 \times 10^{9}} - \frac{1}{1.06 \times 10^{9}}) = « 5.21 \times 10^{7} {J kg}^{- 1} »$ ✓

« multiplies by 3600 kg to get » 1.9 × 10¹¹«J» ✓

Award [2] marks if factor of ½ used, taking into account orbital kinetic energies, leading to a final answer of 9.4 x 10¹⁰«J».

Allow ECF from MP1

Award [2] marks for a bald correct answer.

Syllabus sections

D. Fields » D.1 Gravitational fields

Question 21M.2.HL.TZ2.10

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