A students measures the distance traversed in free fall of a body, the initially at rest, in a given time. He uses this data to

Q: A students measures the distance traversed in free fall of a body, the 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

b From, the, relation $h = ut = \frac{1}{2}g{t^2}$ $h = \frac{1}{2}g{t^2}$$ \Rightarrow g = \frac{{2h}}{{{t^2}}}$ (body, initially, at, rest) Taking, natural, log aritham, on, both, sides, we, get $In\,g = In\,h - 2\,In\,t$ Differentiating, $\frac{{\Delta h}}{g} = \frac{{\Delta h}}{h}\, - 2\,\frac{{\Delta t}}{t}$ For, max imum, permissible, error, or,${\left( {\frac{{\Delta g}}{g} \times 100} \right)_{\max }} = \left( {\frac{{\Delta h}}{h} \times 100} \right) + 2 \times \left( {\frac{{\Delta t}}{t} \times 100} \right)$ According, to, problem $\frac{{\Delta h}}{h} \times 100{ = _{{e_1}}}\,and\,\frac{{\Delta t}}{t} \times 100{ = _{{e_2}}}$ Therefore, $( {\frac{{\Delta g}}{g} \times 100} )_{\max } = {e_1} + 2{e_2}$

SECTION - A [PHYSICS MCQ]

GSEB - English Medium

A students measures the distance traversed in free fall of a body, the 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$e_1+2{e_2}$
C$e_1+e_2$
D$e_1-2{e_2}$

AIPMT 2010, Medium

STD 11 Science
JEE
STD 11 - 1. units,dimensions and measurement
Physics

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