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← JEE Advanced 2017 · Paper 2
PhysicsSingle correct+3 / -1Question 7 of 54

JEE Advanced 2017 · Paper 2, Physics question 7

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\delta T = 0.01 seconds and he measures the depth of the well to be L=20L = 20 meters. Take the acceleration due to gravity g=10 ms−2g = 10\ \mathrm{ms^{-2}} and the velocity of sound is 300 ms−1300\ \mathrm{ms^{-1}}. Then the fractional error in the measurement, δL/L\delta L/L, is closest to

Choose one option
Answer and worked solution

Official answer: B

Total time.
T=2Lg+Lv=2+115 s.T=\sqrt{\frac{2L}g}+\frac Lv=2+\frac1{15}\text{ s}.

Sensitivity.
dTdL=12gL+1v=120+1300=16300.\frac{dT}{dL}=\frac1{\sqrt{2gL}}+\frac1v=\frac1{20}+\frac1{300}=\frac{16}{300}.

Error.
δL=0.01×30016=0.1875 m,δLL≈0.94%≈1%.\delta L=\frac{0.01\times300}{16}=0.1875\text{ m},\qquad\frac{\delta L}L\approx0.94\%\approx1\%.

(B)

Topics:Errors in measurementMotion in a straight line
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