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Q.

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=10 ms–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

0.2%

b

1%

c

3%

d

5%

answer is B.

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Detailed Solution

T=2Lg+LV  T=L5+L300 dT=1512L−1/2dL+(1300dL)dT=125120dL+dL300=0.01dL(120+1300)=0.01dL[15300]=0.01dL=316dLL×100=316×120×100=1516≃1%
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