Practice Gravitational Field in Physics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

A gravitational field is the region around a mass where another mass experiences a gravitational force.

A planet creates an invisible pull around it. The closer you are, the stronger that pull is.

Showing a random 20 of 50 problems.

Example 1

hard

Estimate the gravitational field on the surface of a neutron star:

M = 1.4 M_\odot = 2.8\times 10^{30}\,\text{kg}

r = 1.0\times 10^4\,\text{m}

Example 2

medium

At what height above Earth's surface (

R=6.4\times10^6 \text{ m}

) is the field one quarter of the surface value?

Example 3

hard

At Earth's surface a person weighs

700\,\text{N}

. The same person stands on a tower at altitude

h = 2.0\times 10^6\,\text{m}

. Find their weight there. Use

R_E = 6.4\times 10^6\,\text{m}

Example 4

challenge

On planet Z, a pendulum's period is

\sqrt{2}

times its period on Earth (same length). Find planet Z's surface field given Earth's is

9.8 \text{ N/kg}

Example 5

medium

At what distance from Earth's center is the field

g = 2.45\,\text{N/kg}

? Use

g_{surf} = 9.8\,\text{N/kg}

R = 6.4\times 10^6\,\text{m}

Example 6

hard

A spherical asteroid has mass

M = 1.0\times 10^{15}\,\text{kg}

and radius

r = 5\,\text{km}

. Find the surface field.

Example 7

easy

A planet has

M = 3\times 10^{23}\,\text{kg}

and radius

r = 2\times 10^6\,\text{m}

. Find its surface field. (

G = 6.67\times 10^{-11}

)

Example 8

medium

A satellite is at

r = 7\times10^6 \text{ m}

from Earth's centre (

M=6\times10^{24}

G=6.67\times10^{-11}

). Find the field there.

Find the gravitational field g at r = 7×10⁶ m from Earth's centre

Example 9

easy

Does the gravitational field at a point depend on the mass of any test object placed there?

Example 10

easy

The gravitational field at a point is

5 \text{ N/kg}

. Find the force on a

3 \text{ kg}

mass there.

Field g = 5 N/kg acts on the 3 kg mass — find the gravitational force F

Example 11

challenge

Two stars of mass

M

each are a distance

d

apart. Find the gravitational field at the midpoint between them.

Gravitational fields from two equal masses M are equal and opposite at the midpoint — net field = 0

Example 12

challenge

Two stars of masses

M

and

2M

separated by distance

L

orbit their common center of mass. At the center of mass, find the magnitude of the total gravitational field.

Example 13

medium

Planet X has twice Earth's mass and the same radius. Compare its surface field to Earth's

9.8 \text{ N/kg}

Example 14

easy

State the SI unit of gravitational field strength in two equivalent forms.

Example 15

easy

Distinguish

g

and

G

g = GM/r^2

. Which is the universal constant?

Example 16

easy

A satellite orbits at altitude

h = R

above a planet of radius

R

. By what factor is the field weaker than at the surface?

Example 17

medium

A free-fall accelerometer reads

a = 1.6\,\text{m/s}^2

on a planet. What is the local gravitational field strength?

Example 18

medium

A point lies

r_1 = 3\times 10^8\,\text{m}

from Earth (

M_E = 6\times 10^{24}\,\text{kg}

) and

r_2 = 1\times 10^8\,\text{m}

from the Moon (

M_M = 7.3\times 10^{22}\,\text{kg}

) on the line between them. Find the Earth-produced field at that point. (

G = 6.67\times 10^{-11}

)

Example 19

medium

A planet has the same density as Earth but twice the radius. Find its surface field relative to Earth.

Example 20

medium

Inside a uniform spherical shell, what is the gravitational field due to the shell alone?

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