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Question 19M.2.HL.TZ1.5b.i

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Date May 2019 Marks available [Maximum mark: 3] Reference code 19M.2.HL.TZ1.5b.i
Level HL Paper 2 Time zone TZ1
Command term Show that Question number b.i Adapted from N/A
b.i.
[Maximum mark: 3]
19M.2.HL.TZ1.5b.i
(b.i)

The orbital period T of a moon orbiting a planet of mass M is given by

R 3 T 2 = k M

where R is the average distance between the centre of the planet and the centre of the moon.

Show that  k = G 4 π 2

[3]

Markscheme

ALTERNATE 1

«using fundamental equations»

use of Universal gravitational force/acceleration/orbital velocity equations ✔

equating to centripetal force or acceleration. ✔

rearranges to get k = G 4 π 2   ✔

ALTERNATE 2

«starting with  R 3 T 2 = k M »

substitution of proper equation for T from orbital motion equations ✔

substitution of proper equation for M OR R from orbital motion equations ✔

rearranges to get k = G 4 π 2   ✔

Examiners report

This was another “show that” derivation. Many candidates attempted to work with universal gravitation equations, either from memory or the data booklet, to perform this derivation. The variety of correct solution paths was quite impressive, and many candidates who attempted this question were able to receive some marks. Candidates should be reminded on “show that” questions that it is never allowed to work backwards from the given answer. Some candidates also made up equations (such as T = 2𝝿r) to force the derivation to work out.

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