IB Physics HL D.1 Gravitational fields Question Bank

A space probe of mass 95 kg is designed to land on the surface of an asteroid. The gravitational field strength g of the asteroid at its surface is $2.7 \times 10^{-3} \mathrm{~ms}^{-2}$.

Venus is a planet in the Solar System. The following data are given:

Orbital period of Venus =225 days
Orbital period of Earth =365 days

Which graph shows how the total energy E of an orbiting satellite varies with distance r from the centre of the Earth, where $r_{\mathrm{E}}$ is the radius of the Earth?

The sketch graph shows how the gravitational potential V of a planet varies with distance r from the centre of the planet of radius $R_{0}$.

The magnitude of the gravitational field strength at the point r=R equals the

A planet is in a circular orbit around a star. The speed of the planet is constant. The following data are given:

A satellite in close-Earth orbit moves to an orbit further from the Earth's surface. Which of the following concerning the speed of the satellite and its gravitational potential energy in the new orbit is correct?

A field line is normal to an equipotential surface

The magnitude of the potential at the surface of a planet is V. What is the escape speed from the surface of the planet?

There is a proposal to power a space satellite X as it orbits the Earth. In this model, X is connected by an electronically-conducting cable to another smaller satellite Y .

B4. This question is in three parts. Part 1 is about gravitational fields. Part 2 is about electric current and resistance. Part 3 is about atomic energy levels.

Part 1 Gravitational fields
(a) State Newton's universal law of gravitation.
(b) Deduce that the gravitational field strength g at the surface of a spherical planet of uniform density is given by

where M is the mass of the planet, R is its radius and G is the gravitational constant. You can assume that spherical objects of uniform density act as point masses.
(c) The gravitational field strength at the surface of Mars $g_{\mathrm{M}}$ is related to the gravitational field strength at the surface of the Earth $g_{\mathrm{E}}$ by

The radius of Mars $R_{\mathrm{M}}$ is related to the radius of the Earth $R_{\mathrm{E}}$ by

Determine the mass of Mars $M_{\mathrm{M}}$ in terms of the mass of the Earth $M_{\mathrm{E}}$.
Part 2 Electric current and resistance

The graph below shows how the current I in a tungsten filament lamp varies with potential difference V across the lamp.

(a) (i) Define the electrical resistance of a component.
(ii) Explain whether or not the filament obeys Ohm's law.

(b) Calculate the resistance of the filament lamp when the potential difference across it is 2.8 V .
(c) Two identical filament lamps are connected in series with a cell of emf 6.0 V and negligible internal resistance. Using the graph opposite, calculate the total power dissipated in the circuit.
Part 3 Atomic energy levels
(a) Describe the de Broglie hypothesis.

(b) Outline how atomic emission spectra provide evidence for the quantization of energy in atoms.
(c) Consider an electron confined in a one-dimensional "box" of length L. The de Broglie waves associated with the electron are standing waves with wavelengths given by $\frac{2 L}{n}$, where $n=1,2,3 \ldots$

Show that the energy $E_{n}$ of the electron is given by

where h is Planck's constant and $m_{\mathrm{e}}$ is the mass of the electron.
(d) An electron is confined in a "box" of length $L=1.0 \times 10^{-10} \mathrm{~m}$ in the n=1 energy level. Its position as measured from one end of the box is $(0.5 \pm 0.5) \times 10^{-10} \mathrm{~m}$. Determine
(i) the momentum of the electron.
(ii) the uncertainty in the momentum.