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## Homework Statement

[/B]

The surface tension (T) is measured by capillary rise formula [tex] T = \frac {rh ρg}{2 cos\Theta} [/tex] . The quantities of ρ, g and θ are taken from the table of constants while the height and diameter are measured as

h = (3.00 + 0.01)cm and

D = (0.250 ± 0.001)cm

Find the percentage error in T

My answer came out to be 1.1 % but doesn't coincide with the answer given (0.7 %).

Thanks for any help!

## Homework Equations

According to the book I refer, the equation for error in product or quotient is -[/B]

[tex]\frac{\Delta Z} {Z}= \frac {\Delta A} {A} +\frac {\Delta B} {B} [/tex]

**where Δz/z, Δa/a and Δb/b are relative errors (letters in deltas present uncertainty in measurement)**

## The Attempt at a Solution

I have attempted the solution but have failed to acquire the given answer. Here's what I tried

Acc. to [tex]\frac{\Delta Z} {Z}= \frac {\Delta A} {A} +\frac {\Delta B} {B} [/tex]

we ignore constants (ρ, Θ and g)

h = (3.00 + 0.01)cm

D = (0.250 ± 0.001)cm

so r = D/2 or r = (0.125 ± 0.001)cm

so

[tex]\frac{\Delta T} {T}= \frac {\Delta r} {r} +\frac {\Delta h} {h} [/tex]

which gives,

[tex]\frac{\Delta T} {T} =\frac {0.001} {0.125} +\frac {0.01} {3.00} [/tex]

or,

[tex]\frac{\Delta T} {T} =0.0080 + 0.0034[/tex]

or,

[tex]\frac{\Delta T} {T} =0.0113[/tex]

where

[tex]\frac{\Delta T} {T}[/tex] is relative error. When we multiply that by 100, we get percent error

therefore percent error = 1.13 %

while the answer given is 0.7 %

**please help**