Question

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. $e_2-e_1$
• B. $e_1+2e_2$
• C. $e_1+e_2$
• D. $e_1-2e_2$

Answer 1

The correct option is B $e_1+2e_2$

Distance $s=ut+\frac{1}{2}g{t}^2$

$=\frac{1}{2}g{t}^2$ (because it starts from rest)

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

Net % error in $g=1\times e_1+2\times e_2=e_1+2e_2$