A student measures distance traversed in free fall of a body, initially at rest in a given time. He

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1.Units, Dimensions and Measurement

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A student measures the distance traversed in free fall of a body, initially at rest in a given time. He uses this data to estimate $g$, the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are $e_1$ and $e_2$ respectively, the percentage error in the estimation of $g$ is

A

$e_1 + 2e_2$

B

$e_1 + e_2$

C

$e_1 -2e_2$

D

$e_2 -e_1$

Solution

$\mathrm{h}=\frac{1}{2} \mathrm{gt}^{2} \Rightarrow \mathrm{g}=\frac{2 \mathrm{h}}{\mathrm{t}^{2}}$

then $\quad \frac{{\Delta g}}{g} \times 100 = \left( {\frac{{\Delta h}}{h} + 2\frac{{\Delta t}}{t}} \right) \times 100$

$ = {e_1} + 2{e_2}$

Standard 11

Physics

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