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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 dT = 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, dL / 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=T2gdL2L=dT dLV≈012gdLL=dTL=12gT2T=2Lg=2×2010≈2sdTT=dL2gL×g2L=dLL12dLL=2dTT=2×0.012=0.01
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