A person measures  the   depth of  a well by  measuring  the time interval between  drooping   a  stone  and  receiving the  sound  of  impact  with  the  bottom  of  the well.The  error in his measurement of time is  $\delta T=0.01$ seconds and he   measures the depth of  the well to be  L =20 meters  take the  acceleration  due  to gravity $g=10m/s^2$  and the  velocity  of  sound  is   300 m/s . Then  the  fractional  error in the   measurement, $\delta L/L,$ is closest to  

Given that a person measures the depth of  awell by measuring the interval between  dropping a stone and receiving the sound of impact with the bottom of the well. 
The error in his measurement of  time is  $\delta T=0.01\sec onds$
Depth of  the well measured , L=20 times
Total time taken to hear the sound = time of free fall of the stone+time taken for sound to travel up. 
$$\begin{gathered} \Rightarrow t=\sqrt{\frac{2L}{g}}+\frac{L}{C} \\ \Rightarrow \frac{dt}{dL}=\sqrt{\frac{2}{g}}\times \frac{d}{dL}\left(\sqrt{L}\right)+\frac{1}{C}\frac{dL}{dL} \\ \Rightarrow \frac{dt}{dL}=\sqrt{\frac{2}{g}}\times \frac{1}{2\sqrt{L}}+\frac{1}{C}\frac{dL}{dL} \\ dL=\frac{dt}{\frac{1}{\sqrt{2gL}}+\frac{1}{C}} \\ \Rightarrow \frac{dL}{L}\times 100=\left(\frac{dt}{\frac{1}{\sqrt{2gL}}+\frac{1}{C}}\right)\frac{1}{L}\times 100 \end{gathered}$$

Percentage error in measurement in depth of well = $\frac{15}{16}\approx 1\%$