Physics 9702/42 — October/November 2017

Cambridge A-Level · A Level Structured Questions · worked solutions for every part, with the mark scheme

questions

100

marks

120

minutes

Topics Motion in a Circle · Electric Fields · Magnetic Fields · Gravitational Fields · Temperature · Thermodynamics · +7 more

Q1Gravitational FieldsMotion in a CircleFree sample

(a)

State Newton’s law of gravitation.

(b)

The planet Jupiter and one of its moons, Io, may be considered to be uniform spheres that are isolated in space.
Jupiter has radius $R$ and mean density $\rho$ .
Io has mass $m$ and is in a circular orbit about Jupiter with radius $nR$ , as illustrated in Fig. 1.1.

Fig. 1.1

The time for Io to complete one orbit of Jupiter is $T$ .

Show that the time $T$ is related to the mean density $\rho$ of Jupiter by the expression

\rho T^2 = \frac{3\pi n^3}{G}

where $G$ is the gravitational constant.

(c)

(i)

The radius $R$ of Jupiter is $7.15 \times 10^4\ \text{km}$ and the distance between the centres of Jupiter and Io is $4.32 \times 10^5\ \text{km}$ .
The period $T$ of the orbit of Io is $42.5$ hours.

Calculate the mean density $\rho$ of Jupiter.

$\rho$ = ______ $\text{kg m}^{-3}$

(ii)

The Earth has a mean density of $5.5 \times 10^3\ \text{kg m}^{-3}$ . It is said to be a planet made of rock.
By reference to your answer in (i), comment on the possible composition of Jupiter.

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Q7Electronics10M
Q8Magnetic Fields7M
Q9Magnetic Fields · Electric Fields9M
Q10Quantum Physics5M
Q11Alternating Currents11M
Q12Nuclear Physics11M

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