Q27 · 2022 · Paper 1Complex unfamiliar5 marks
QUESTION 27 (5 marks)
Object A is five times the mass of object B. The graph shows the contribution of each object towards the strength of the net gravitational field between them.
Determine the total distance between the centre of the two objects. Show your working.
WORKED SOLUTION
5 marksQCAA guide · typeset solution
ANSWER
See worked solution below.
Worked solution
Point where lines intersect indicates distance from centre
of A where net gravitational field strength is equal to zero.
35;
35
r
rB
A
x
=
=
−
(
)
(
)
3
2
2
2
2
2
2
0
5
35
5
35
35
5
35
35
5
35
35
5
50
2
.7
g
gB
A
g
g
GM
GMB
r
rB
M
M
B
B
B
A
A
x
x
x
A
x
−
=
=
=
=
−
=
−
=
−
=
+
=
Total distance = 51 × 107 m (to two significant figures)
• recognises the scenario relates to gravitational
field strength [1 mark]
• identifies distance from A where net gravitational
field strength is zero [1 mark]
• constructs an equation that can be solved for the
distance between the objects [1 mark]
• provides appropriate mathematical reasoning
[1 mark]
• determines the distance between the centre of
the two objects [1 mark]
One QCAA sample method typeset for web; criterion wording is adapted from the official marking guide.
How many marks did you earn?
Compare your working with the guide above.