Physics 9702 · AS & A Level · Gravitational potential

Gravitational potential — practice question

Mars can be treated as a lone sphere with diameter $6.79 \times 10^{6}\,\text{m}$, and its mass of $6.42 \times 10^{23}\,\text{kg}$ is assumed to be concentrated at the centre. A rock with mass $1.40\,\text{kg}$ is at rest on the Martian surface.
(a(i))[3]

Find its weight.

(a(ii))[2]

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

(b)[3]

Use the information in (a)(ii) to find the speed the rock must have as it leaves the Martian surface in order to escape the planet’s gravitational attraction.

(c(i))[2]

Determine the temperature at which the root-mean-square (r.m.s.) speed of hydrogen molecules is the same as the speed found in (b). Hydrogen may be treated as an ideal gas. A molecule of hydrogen has a mass of $2\,\text{u}$. The mean translational kinetic energy $\langle E_{K} \rangle$ of a molecule of an ideal gas is given by $\langle E_{K} \rangle = \frac{3}{2} kT$, where $T$ is the thermodynamic temperature of the gas and $k$ is the Boltzmann constant.

(c(ii))[2]

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

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: Application of the gravitational formula $W = \dfrac{GMm}{r^2}$ together with correct substitution

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