DP Physics (last assessment 2024)

Question 18M.2.HL.TZ2.6

Date	May 2018	Marks available	[Maximum mark: 11]	Reference code	18M.2.HL.TZ2.6
Level	HL	Paper	2	Time zone	TZ2
Command term	Calculate, Draw, Estimate, Show that, State	Question number	6	Adapted from	N/A

[Maximum mark: 11]

18M.2.HL.TZ2.6

A planet has radius R. At a distance h above the surface of the planet the gravitational field strength is g and the gravitational potential is V.

(a.i)

State what is meant by gravitational field strength.

[1]

Markscheme

the «gravitational» force per unit mass exerted on a point/small/test mass

[1 mark]

(a.ii)

Show that V = –g(R + h).

[2]

Markscheme

at height h potential is V = – $\frac{{GM}}{{(R + h)}}$

field is g = $\frac{{GM}}{{{{(R + h)}^2}}}$

«dividing gives answer»

Do not allow an answer that starts with g = – $\frac{{\Delta V}}{{\Delta r}}$ and then cancels the deltas and substitutes R + h

[2 marks]

(a.iii)

Draw a graph, on the axes, to show the variation of the gravitational potential V of the planet with height h above the surface of the planet.

[2]

Markscheme

correct shape and sign

non-zero negative vertical intercept

M18/4/PHYSI/HP2/ENG/TZ2/06.a.iii/M

[2 marks]

(b)

A planet has a radius of 3.1 × 10⁶ m. At a point P a distance 2.4 × 10⁷ m above the surface of the planet the gravitational field strength is 2.2 N kg^–1. Calculate the gravitational potential at point P, include an appropriate unit for your answer.

[1]

Markscheme

V = «–2.2 × (3.1 × 10⁶ + 2.4 × 10⁷) =» «–» 6.0 × 10⁷ J kg^–1

Unit is essential

Allow eg MJ kg^–¹ if power of 10 is correct

Allow other correct SI units eg m²s^–², N m kg^–¹

[1 mark]

(c)

The diagram shows the path of an asteroid as it moves past the planet.

M18/4/PHYSI/HP2/ENG/TZ2/06.c