IB Physics SL D 1 4 Gravitational Field Strength Questions

Practise IB Physics SL D.1.4 by calculating gravitational field strength and comparing mass, radius and distance in planetary systems.

Exam points

Define gravitational field strength as force per unit mass on a small point mass.
Derive g = GM/r² from g = F/m and Newton’s gravitational-force formula, cancelling test mass.
Calculate g = GM/r² using source mass and centre-to-point distance, including R + h for a satellite.
Compare fields using source-mass ratios and inverse-square radius or distance ratios.
Combine M ∝ R³ with g ∝ M/R² to compare surface fields of planets with the same density.
Use a = g to compare free-fall or orbital accelerations, distinguishing field strength from force.
Rearrange g = GM/r² to infer a source mass or radius from field measurements.
Equate opposing GM/r² fields at a zero-field point to determine the ratio of two masses.
Compare opposing fields along the line through two masses to determine the net field direction.
Compare a distant body’s gravitational acceleration with the local value to judge its effect.
Calculate GM/r² for a proton, then form a gravitational-to-electric field ratio with units C kg⁻¹.

[Maximum number: 4]

B2. This question is in two parts. Part 1 is about simple harmonic motion and the superposition of waves. Part 2 is about gravitational fields.
Part 1 Simple harmonic motion and the superposition of waves
An object of mass m is placed on a frictionless surface and attached to a light horizontal spring. The other end of the spring is fixed.

Figure for Question IB Physics SL D 1 4 Gravitational Field Strength Questions question 1 — IB Physics SL

The equilibrium position is at B . The direction B to C is taken to be positive. The object is released from position A and executes simple harmonic motion between positions A and C .

(a)

Part 2
Gravitational fields

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(i)

Deduce that the gravitational field strength g at the surface of a spherical planet of uniform density is given by

g=\frac{G M}{R^{2}}

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.

[ 2 ]

(ii)

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

g_{\mathrm{M}}=0.38 \times g_{\mathrm{E}}

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

R_{\mathrm{M}}=0.53 \times R_{\mathrm{E}}

Determine the mass of Mars $M_{\mathrm{M}}$ in terms of the mass of the Earth $M_{\mathrm{E}}$ .

[ 2 ]

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IB Physics SL D 1 4 Gravitational Field Strength Questions question 1

Question (a)

Question (i)

Question (ii)