Gravatational Field Strength problem (Grade 12 physics)

[axxon]

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!

 

[Hootenanny]

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?}

 

[axxon]

it would be 4R wouldn't it?

 

[Hootenanny]

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 ...?

 

[axxon]

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

 

[Hootenanny]

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

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

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,

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

Do you follow?

I can see that it would be 1/2 of g

Correct!

g under these conditions would be 15.5 (1/2) = 7.75 N/kg

You might to recheck the final bit

 

[axxon]

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

 

[Hootenanny]

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

A pleasure