Question

The percentage error in measurement of length and time period is 2% and 1% respectively. the percentage error in measurement of 'g' is

Answer 1

the answer is 4% as percent error is fractional error *100

Answer 2

Answer:

The percentage error in the measurement of g will be 4%.

Step-by-step explanation:

Given in the question -

The percentage error in measurement of length is = 2%

The percentage error in measurement of time period is = 1%

The relation in g, time period T, and length l is given by -

$g = \frac{4\pi ^2l}{T^2}$

So the error in measurement in g will be the sum of the error in measurement in l and 2 times error in measurement of the time period.

$\frac{\Delta g}{g} = \frac{\Delta l}{l} +2(\frac{\Delta T}{T} )$

Now in percentage error -

$\frac{\Delta g}{g}\times 100 = \frac{\Delta l}{l}\times 100 +2(\frac{\Delta T}{T}\times 100 )\\\\\frac{\Delta g}{g}\times 100 = 2\%+2(1\%) = 4\%$

So the percentage error in the measurement of g will be 4%.

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