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JEE Main

Exam: JEE Main
Subject: Physics
Chapter: Mathematics in Physics

JEE Main · Physics · Mathematics in Physics

A student measures the distance traversed in free fall of a body,...

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

Options

A $\mathrm{e}_2-\mathrm{e}_1$
B $e_1+2 e_2$
C $e_1+e_2$
D $e_1-2 e_2$

Correct answer

B. $e_1+2 e_2$

Step-by-step solution

\begin{aligned} & h=\frac{1}{2} g t^2 \\ & \text { or } \quad g=\frac{\mathrm{2h}}{\mathrm{t}^2} \\ & \therefore \quad \log \mathrm{g}=\log \mathrm{h}-2 \log \mathrm{t} \\ & \left(\frac{\Delta g}{g} \times 100\right)_{\max }=\left(\frac{\Delta \mathrm{h}}{\mathrm{h}} \times 100\right)+2\left(\frac{\Delta \mathrm{t}}{\mathrm{t}} \times 100\right) \\ & =\mathrm{e}_1+2 \mathrm{e}_2 \\ & \end{aligned}

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