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NEET 2010
Exam
NEET
Year
2010
Subject
Physics
Chapter
Mathematics in Physics

NEET 2010 · 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 gg, the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are e1e_1 and e2e_2 respectively, the percentage error in the estimation of gg is

Options

  1. Ae2−e1\mathrm{e}_2-\mathrm{e}_1
  2. Be1+2e2e_1+2 e_2
  3. Ce1+e2e_1+e_2
  4. De1−2e2e_1-2 e_2

Correct answer

B. e1+2e2e_1+2 e_2

Step-by-step solution

\begin{aligned} & h=\frac{1}{2} g t^2 \\ & \text{ or } \quad g=\frac{\mathrm{h}}{\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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