A person measures the depth of a well by measuring the time 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 δT=0.01 seconds and he measures the depth of the well to be L=20 meters. Take the acceleration due to gravity g=10ms−2 and the velocity of sound is 300 ms−1. Then the fractional error in the measurement,δL/L , is closest to
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a
1%
b
5%
c
3%
d
0.2%
answer is A.
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Detailed Solution
2Lg+LV=T After differentiating, ⇒2gdL2L+0=dT dLV≈0⇒12gdLL=dT After integrating, ⇒L=12gT2⇒T=2Lg=2×2010=2sA/SO,dLL=2dTT=2×0.012=0.01⇒dLL×100=1%