Q. 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) $e_{1} - 2e_{2}$
Explanation
In $g = \ln{h - 2\ln t}$ $\left( \frac{\mathrm{\Delta}g}{g} \times 100 \right)_{\max} = \frac{\mathrm{\Delta}h}{h} \times 100 + 2\frac{\mathrm{\Delta}t}{t} \times 100 = e_{1} + 2e_{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.