# Gravatational Field Strength problem (Grade 12 physics)

1. Apr 5, 2009

### axxon

1. The problem statement, all variables and given/known data
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.

2. Relevant equations
g= GM /R2

3. 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...

2. Apr 6, 2009

### Hootenanny

Staff Emeritus

Are you sure that this is correct? If you double R, how much does R2 change by?

3. Apr 6, 2009

### axxon

it would be 4R wouldn't it?

4. Apr 6, 2009

### Hootenanny

Staff Emeritus
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. Apr 6, 2009

### axxon

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. Apr 7, 2009

### Hootenanny

Staff Emeritus
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

$$15.5 = \frac{Gm_0}{r_0^2}$$

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,

\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}

Do you follow?

Correct!
You might to recheck the final bit

7. Apr 7, 2009

### axxon

OHH!! That makes it muchh more clear! Thanks a bunch!

8. Apr 7, 2009

### Hootenanny

Staff Emeritus
A pleasure