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

Answer 1

The correct option is A $e_1+2e_2$

%Error in distance measerment $=e_1$

$\%$ Error in time measwrement $=e_2$

Now, formula used :

$g=\frac{2S}{t^2}\{\text{come from :}S=\frac{1}{2}g{t}^2\}$

Now, %error:

$\frac{\Delta g}{g}=\frac{\Delta S}{S}+\frac{\Delta t}{t}\times 2\left\{\begin{array}{c}\text{If}z=\frac{a^x{b}^y}{c^z}\\ \text{then}\frac{\Delta z}{z}=x\frac{\Delta a}{a}+y\frac{\Delta b}{b}+z\frac{\Delta c}{c}\end{array}\right\}$

$\%\frac{\Delta q}{g}=e_1+2e_2$