Calculating Uncertainty: What is the Effect of θ?”

[Janiceleong26]

Homework Statement

Homework Equations

Absolute uncertainty in θ = δθ/θ

The Attempt at a Solution

I know that smaller θ gives smaller actual uncertainty, thus leaving B and D out. The answer is C. but what about option A?

 

[haruspex]

Your relevant equation is wrong.
If the fractional error in X is r, how large is the actual error in X? How large then is the actual error in theta?

 

[Janiceleong26]

Your relevant equation is wrong.
If the fractional error in X is r, how large is the actual error in X? How large then is the actual error in theta?

The actual error in X would be rX? And rθ?

 

[haruspex]

The actual error in X would be rX? And rθ?

Yes. So what is the fractional error in theta?

 

[Janiceleong26]

Yes. So what is the fractional error in theta?

r ?

 

[haruspex]

r ?

Right. Can you now see why A is wrong?

 

[Janiceleong26]

Right. Can you now see why A is wrong?

No ..sorry..
If actual uncertainty in θ is r, then the percentage uncertainty of θ would be r x100 right? Isn't the effect the same?

 

[haruspex]

No ..sorry..
If actual uncertainty in θ is r, then the percentage uncertainty of θ would be r x100 right?

No, the percentage uncertainty is 100x fractional uncertainty.

 

[Janiceleong26]

No, the percentage uncertainty is 100x fractional uncertainty.

What's the difference between fractional uncertainty and fractional error?

 

[haruspex]

What's the difference between fractional uncertainty and fractional error?

Sorry, I didn't notice I had switched from uncertainty to error. For the purposes of this question it makes no difference.
So in your post #5, you have that if the fractional (or percentage) uncertainty in x is r then the fractional (or percentage) uncertainty in theta is r.
Can you see how that conflicts with A?

 

[Janiceleong26]

Sorry, I didn't notice I had switched from uncertainty to error. For the purposes of this question it makes no difference.
So in your post #5, you have that if the fractional (or percentage) uncertainty in x is r then the fractional (or percentage) uncertainty in theta is r.
Can you see how that conflicts with A?

Ohhhh...is it because the percentage uncertainty would be the same for all values of θ, but the uncertainty itself varies?

 

[haruspex]

Ohhhh...is it because the percentage uncertainty would be the same for all values of θ, but the uncertainty itself varies?

Yes.

 

[Janiceleong26]

Yes.

Thanks