Question

the acceleration due to gravity is measured on the surface of earth by using simple pendulum if alpha and beta are the relative error in the measurement of length and time period respectively then the percentage error in the measurement of acceleration due to gravity is

Answer 1

Final Answer :
$( \alpha + 2 \beta )100 \: \%$

Steps :
1) Relative Error in measurement of Length :
$\frac{\Delta L}{L} = \alpha \\ \frac{\Delta T}{T} = \beta$

2) We also know that,
$\frac{\Delta g}{g} = \frac{\Delta L}{L} +2*\frac{\Delta T}{T} \\ \\ => ( \alpha + 2\beta )$

3) Therefore, Percentage Error in g is
$( \alpha + 2 \beta ) \times 100\%$

Answer 2

Relative Error in Length = α

Relative Error in Time = β

% Error in the Acceleration due to gravity = % Error in Length + % Error in Time.

= 100α + 100 × 2β

= 100(α + 2β) %

Hence, % Error in acceleration due to gravity is 100(α + 2β) %.

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