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Date May 2012 Marks available 3 Reference code 12M.2.SL.TZ1.7
Level Standard level Paper Paper 2 Time zone Time zone 1
Command term State Question number 7 Adapted from N/A

Question

Part 2 Gravitational fields

State Newton’s universal law of gravitation.

[3]
a.

Deduce that the gravitational field strength g at the surface of a spherical planet of uniform density is given by

g=GMR2

where M is the mass of the planet, R is its radius and G is the gravitational constant. You can assume that spherical objects of uniform density act as point masses.

[2]
b.

The gravitational field strength at the surface of Mars gM is related to the gravitational field strength at the surface of the Earth gE by

gM = 0.38 × gE.

The radius of Mars RM is related to the radius of the Earth RE by

RM = 0.53 × RE.

Determine the mass of Mars MM in terms of the mass of the Earth ME.

[2]
c.

(i) On the diagram below, draw lines to represent the gravitational field around the planet Mars.

(ii) An object falls freely in a straight line from point A to point B in time t. The speed of the object at A is u and the speed at B is v. A student suggests using the equation v=u+gMt to calculate v. Suggest two reasons why it is not appropriate to use this equation.

[3]
d.

Markscheme

there is an attractive force;
between any two point/small masses;
proportional to the product of their masses;
and inversely proportional to the square of their separation;
Accept formula with all terms defined.

a.

use of g=Fm and F=GmMR2;
evidence of substitution/manipulation;
to get g=GMR2

b.

gMgE=MMR2MMER2EMMME=gMgE×[RMRE]2;

MM(=0.38×0.532ME)=0.11ME;

c.

(i) radial field with arrows pointing inwards;

(ii) field between A and B is not equal to field at surface;
acceleration is not constant between these two points;

d.

Examiners report

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

Syllabus sections

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