Gravatational Field Strength problem (Grade 12 physics)

In summary, in this conversation, the gravitational field strength of an unknown planet was given as 15.5 N/kg on its surface. To calculate the value of "g" if the planet's mass and radius were both doubled, the hint to use variation was given. The attempt at a solution involved using the equation g=GM/R2 and setting up a ratio of M/2M = R2/2R2. This led to the conclusion that doubling the radius divides g by 4, while doubling the mass doubles g. Therefore, the overall effect on g is that it becomes half of the original value, resulting in a final value of 7.75 N/kg.
  • #1
axxon
15
0

Homework Statement


The gravitational field strength of an unknown planet is 15.5 N/kg on its surface. Calculate the value of “g” if the planets mass and radius were both doubled. Hint: Use variation.


Homework Equations


g= GM /R2


The Attempt at a Solution



Well my teacher gave a hint saying use variation so this was my attempt at it:

M / 2M = R2 / 2R2

Now this is where i kind of get stuck. If I simplify M, i am left with:

1/2 = R2 / 2R2

I don't now what i should do next or if i am even on the right track...

Thanks in advanced!
 
Physics news on Phys.org
  • #2
axxon said:

Homework Statement


The gravitational field strength of an unknown planet is 15.5 N/kg on its surface. Calculate the value of “g” if the planets mass and radius were both doubled. Hint: Use variation.


Homework Equations


g= GM /R2


The Attempt at a Solution



Well my teacher gave a hint saying use variation so this was my attempt at it:

M / 2M = R2 / 2R2

Are you sure that this is correct? If you double R, how much does R2 change by?
 
  • #3
it would be 4R wouldn't it?
 
  • #4
axxon said:
it would be 4R wouldn't it?
Indeed it would. So now you have a simple ratio question. Doubling the radius divides g by 4, doubling the mass doubles g, so the overall effect on g is ...?
 
  • #5
Hootenanny said:
Indeed it would. So now you have a simple ratio question. Doubling the radius divides g by 4, doubling the mass doubles g, so the overall effect on g is ...?

But how does doubling the radius dividing g by four and same with mass?


I can see that it would be 1/2 of g or g under these conditions would be 15.5 (1/2) = 7.75 N/kg
 
  • #6
axxon said:
But how does doubling the radius dividing g by four and same with mass?
Okay, let's take it step by step.

You are given that the acceleration due to gravity on the surface of a planet with radius r=r0 and mass m = m0 is g=15.5 N/kg. In other words, you know that

[tex]15.5 = \frac{Gm_0}{r_0^2}[/tex]

Now, you are asked to determine the value of g if the radius of the planet was r=2r0 and it's mass was m=2m0. That is if both the radius and the mass are doubled. So using Newton's law of gravitation,

[tex]\begin{aligned}
g & = \frac{G\left(2m_0\right)}{\left(2r_0\right)^2}\\
& = \frac{2}{4}\underbrace{\frac{G m_0}{r_0^2}}_{15.5}\\
& = \frac{1}{2}15.5\\
g & = 7.25 \;N/kg
\end{aligned}[/tex]

Do you follow?

axxon said:
I can see that it would be 1/2 of g
Correct!
axxon said:
g under these conditions would be 15.5 (1/2) = 7.75 N/kg
You might to recheck the final bit :wink:
 
  • #7
OHH! That makes it muchh more clear! Thanks a bunch!
 
  • #8
axxon said:
OHH! That makes it muchh more clear! Thanks a bunch!
A pleasure :smile:
 

1. What is gravitational field strength?

Gravitational field strength, also known as gravitational acceleration, is a measure of the force of gravity acting on a mass within a certain gravitational field. It is typically denoted by the symbol g and is measured in units of meters per second squared (m/s^2).

2. How is gravitational field strength calculated?

The gravitational field strength at a certain point is calculated by dividing the force of gravity acting on an object at that point by the mass of the object. This can be expressed as g = F/m, where g is the gravitational field strength, F is the force of gravity, and m is the mass of the object.

3. What factors affect gravitational field strength?

The main factor that affects gravitational field strength is the mass of the object creating the gravitational field. The larger the mass, the stronger the gravitational field. Additionally, the distance from the object also affects gravitational field strength, with the field becoming weaker as distance increases.

4. How does gravitational field strength differ on different planets?

Gravitational field strength varies on different planets due to differences in mass and radius. For example, the gravitational field on Earth is 9.8 m/s^2, while on Mars it is only 3.7 m/s^2. This means that a person would feel lighter on Mars compared to Earth due to the weaker gravitational pull.

5. How is gravitational field strength related to potential energy?

Gravitational field strength and potential energy are inversely proportional. This means that as gravitational field strength decreases (e.g. when moving away from a massive object), potential energy increases. This relationship is described by the formula PE = mgh, where PE is potential energy, m is mass, g is gravitational field strength, and h is height.

Similar threads

  • Introductory Physics Homework Help
Replies
23
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
670
  • Introductory Physics Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
21
Views
2K
  • Introductory Physics Homework Help
Replies
17
Views
2K
  • Introductory Physics Homework Help
Replies
9
Views
3K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
1K
Back
Top