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A student measure the distance traversed in freely fall of a body initially at rest in a given time. He uses this data to estimate the acceleration due to gravity (g). If the maximum percentage error in measurement of the distance and the time are e₁ and e₂ respectively. The percent age error in the estimation of g is

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$e_{1} + 2 e_{2}$

$e_{1} + e_{2}$

$e_{1} - 2 e_{2}$

$e_{2} - e_{1}$

answer is A.

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Detailed Solution

$g = \frac{t^{2}}{2 h}$

$% (∆ g) = % (∆ h) + 2 \times % (∆ t) = e_{1} + 2 e_{2}$

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