The planet Mars may be considered to be an isolated sphere of diameter $6.79 \times 10^{6}\ \text{m}$ with its mass of $6.42 \times 10^{23}\ \text{kg}$ concentrated at its centre. A rock of mass $1.40\ \text{kg}$ rests on the surface of Mars. For this rock, (i) determine its weight, weight = \_\_\_\_\_\_ $\text{N}$ (ii) show that its gravitational potential energy is $-1.77 \times 10^{7}\ \text{J}$. (b) Use the information in (a)(ii) to determine the speed at which the rock…

Physics 9702/43 — October/November 2011

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

questions

100

marks

120

minutes

Topics Medical Physics · Gravitational Fields · Ideal Gases · Temperature · Oscillations · Capacitance · +7 more

Q1Gravitational FieldsIdeal GasesFree sample

The planet Mars may be considered to be an isolated sphere of diameter $6.79 \times 10^{6}\ \text{m}$ with its mass of $6.42 \times 10^{23}\ \text{kg}$ concentrated at its centre.
A rock of mass $1.40\ \text{kg}$ rests on the surface of Mars.

For this rock,

(a)

(i)

determine its weight,

weight = ______ $\text{N}$

(ii)

show that its gravitational potential energy is $-1.77 \times 10^{7}\ \text{J}$ .

(b)

Use the information in (a)(ii) to determine the speed at which the rock must leave the surface of Mars so that it will escape the gravitational attraction of the planet.

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

(c)

The mean translational kinetic energy $\langle E_K \rangle$ of a molecule of an ideal gas is given by the expression

\langle E_K \rangle = \frac{3}{2} kT

where $T$ is the thermodynamic temperature of the gas and $k$ is the Boltzmann constant.

(i)

Determine the temperature at which the root-mean-square (r.m.s.) speed of hydrogen molecules is equal to the speed calculated in (b).
Hydrogen may be assumed to be an ideal gas.
A molecule of hydrogen has a mass of $2\ \text{u}$ .

temperature = ______ $\text{K}$

(ii)

State and explain one reason why hydrogen molecules may escape from Mars at temperatures below that calculated in (i).

The rest of this paper

11 more questions

Q2Temperature6M
Q3Oscillations9M
Q4Capacitance9M
Q5Alternating Currents6M
Q6Magnetic Fields · Motion in a Circle12M
Q7Quantum Physics10M
Q8Nuclear Physics6M
Q9Electronics7M
Q10Medical Physics6M
Q11Medical Physics9M
Q12Communication8M

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