Question

018: Find the percentage error in the density of
a body when the mass is uncertain by
+-2% & length by ± 1%​

Answer 1

AnsweAlright, let’s do it!

We know that…

ρ=ml3

Where ρ

is density, m is mass, and l

is length

Before I continue

We have stated that the mass has an error of 2%

of its true value, and the length has an error of 1%

of its true value. So let’s come up with two things to qualify this.

Let’s say that we have a measured value, which is.

me=e1m

le=e2l

Where e1

and e2 are coefficients of the error. It didn’t say whether the measurements were high or low, so I’ll just say e1=.98,1.02, e2=.99,1.01

Now, let’s plug in…

ρe=e1m(e2l)3=e1e32ml3=e1e32ρ

So, now we want ρeρ−1=e1e32−1=(e1e32−1)∗100%

There are four different possibilities for this, depending on whether your errors are high or low. and for which measurement. One of the worse case scenarios is about 5%.

r:

Explanation:

Answer 2

Explanation:

ρ=ml3  

Where  ρ  is density,  m  is mass, and  l  is length

Before I continue

We have stated that the mass has an error of  2%  of its true value, and the length has an error of  1%  of its true value. So let’s come up with two things to qualify this.

Let’s say that we have a measured value, which is.

me=e1m  

le=e2l  

Where  e1  and  e2  are coefficients of the error. It didn’t say whether the measurements were high or low, so I’ll just say  e1=.98,1.02 ,  e2=.99,1.01  

Now, let’s plug in…

ρe=e1m(e2l)3=e1e32ml3=e1e32ρ  

So, now we want  ρeρ−1=e1e32−1=(e1e32−1)∗100%  

There are four different possibilities for this, depending on whether your errors are high or low. and for which measurement. One of the worse case scenarios is about 5%.