a person measures the depth of a well by measuring the time interval of dropping a stone and recieving the - Physics - Units And Measurements

Question

a person measures the depth of a well by measuring the time
interval of dropping a stone and recieving the sound impact with
the bottom of the well the error in his measurement of time t is 0
01sec and he measures the well to be L=20mtrs, take the accerlation
due to gravity is 10m/s2 and velocity of sound is 300m/s then find
the fractional error in the measurement deltaL/l is closest to

Vijay Shankar Yadav · Accepted Answer

Dear Student,
According to question L=12gt12t1=2Lg---1and L=300t2t2=L300---2add 1 and 2 we gett=2Lg+L300----3put the valu of parameters we get t=2×2010+20300=2+
07=2
07now take log of 3 and partilly differentiate we get ∆tt=1g×∆LL+1300×∆LL∆tt=(1g+1300)×∆LL∆LL=∆tt(1g+1300)=
012 07(110+1300)=0 046=0 05
Regards