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

Question

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

Infinity Learn · Accepted Answer

$$2Lg+LV=T2gdL2L=dT$$ dLV≈$$012gdLL=dTL=12gT2T=2Lg=2$$×$$2010$$≈$$2sdTT=dL2gL$$×$$g2L=dLL12dLL=2dTT=2$$×$$0.012=0.01$$

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