Physics 9702/42 — February/March 2022

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

questions

100

marks

120

minutes

Topics Gravitational Fields · Quantum Physics · Nuclear Physics · Medical Physics · Motion in a Circle · Thermodynamics · +8 more

Q1Gravitational FieldsMotion in a CircleFree sample

(a)

The point P in Fig. 1.1 represents a point mass.

On Fig. 1.1, draw lines to represent the gravitational field around P.

Fig. 1.1

(b)

A moon is in circular orbit around a planet.

Explain why the path of the moon is circular.

(c)

Many moons are in circular orbit about a planet.

The angular velocity of a moon is $\omega$ when the orbit of the moon has a radius $r$ about the planet.

Fig. 1.2 shows the variation of $r^3$ with $1/\omega^2$ for these moons.

Fig. 1.2

(i)

Show that the mass $M$ of the planet is given by the expression

M = \frac{\text{gradient}}{G}

where $G$ is the gravitational constant.

(ii)

Use Fig. 1.2 and the expression in (c)(i) to show that the mass $M$ of the planet is $1.0 \times 10^{26}\ \text{kg}$ .

(iii)

Determine the speed of a moon in orbit around the planet with an orbital radius of $1.2 \times 10^8\ \text{m}$ .

speed = ______ $\text{m s}^{-1}$

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