A student performs an experiment to determine the Young's modulus of a wire, exactly 2 m long, by Searle's method. In a particular reading, the student measures the extension in the length of the wire to be 0.8 mm with an uncertainty of ±0.05 mm at a load of exactly 1.0 kg. The student also measures the diameter of the wire to be 0.4 mm with an uncertainty of ±0.01 mm. Take g=9.8 ms−2 (exact). The Young's modulus obtained from the reading is

Name: Video solution 1: A student performs an experiment to determine the Young's modulus of a wire, exactly 2 m long, by Searle's method. In a particular reading, the student measures the extension in the length of the wire to be 0.8 mm with an uncertainty of ±0.05 mm at a load of exactly 1.0 kg. The student also measures the diameter of the wire to be 0.4 mm with an uncertainty of ±0.01 mm. Take g=9.8 ms−2 (exact). The Young's modulus obtained from the reading is
Uploaded: 2023-01-27T17:21:04.000Z
Duration: 2 min

Young's modulus Y=AlFL=πd2l4FL=π(0.4×10−3)2(0.8×10−3)(4)(1.0×9.8)(2)=2.0×1011Nm−2∴ΔY={2(dΔd)+(lΔl)}Y={2×0.40.01+0.80.05}×2.0×1011=0.2×1011Nm−2Or YΔY=2(dΔd)+(lΔl)Or(Y+ΔY)=(2±0.2)×1011Nm−2

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A student performs an experiment to determine the Young's modu

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A student performs an experiment to determine the Young's modulus of a wire, exactly $2 m$ long, by Searle's method. In a particular reading, the student measures the extension in the length of the wire to be $0.8 mm$ with an uncertainty of $\pm 0.05 mm$ at a load of exactly $1.0 kg$ . The student also measures the diameter of the wire to be $0.4 mm$ with an uncertainty of $\pm 0.01 mm$ . Take $g = 9.8 ms^{- 2}$ (exact). The Young's modulus obtained from the reading is

(2.0 \pm 0.3) \times 1 0^{11} Nm^{- 2}

(2.0 \pm 0.2) \times 1 0^{11} Nm^{- 2}

(2.0 \pm 0.1) \times 1 0^{11} Nm^{- 2}

(2.0 \pm 0.05) \times 1 0^{11} Nm^{- 2}

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Updated on: Jan 27, 2023

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Samuel Discussed

A student performs an experiment to determine the Young's modulus of a wire, exactly

2 m

long, by Searle's method. In a particular reading, the student measures the extension in the length of the wire to be

0.8 mm

with an uncertainty of

\pm 0.05 mm

at a load of exactly

1.0 kg

. The student also measures the diameter of the wire to be

0.4 mm

with an uncertainty of

\pm 0.01 mm

. Take

g = 9.8 ms^{- 2}

(exact). The Young's modulus obtained from the reading is

15 mins ago

Discuss this question LIVE

15 mins ago

Text solutionVerified

Young's modulus

Y = \frac{F L}{A l} = \frac{4 F L}{π d ^{2} l}

= \frac{( 4 ) ( 1.0 \times 9.8 ) ( 2 )}{π ( 0.4 \times 1 0 ^{- 3} ) ^{2} ( 0.8 \times 1 0 ^{- 3} )} = 2.0 \times 1 0^{11} Nm^{- 2}

∴ Δ Y = {2 (\frac{Δ d}{d}) + (\frac{Δ l}{l})} Y = {2 \times \frac{0.01}{0.4} + \frac{0.05}{0.8}} \times 2.0 \times 1 0^{11} = 0.2 \times 1 0^{11} Nm^{- 2}

\frac{Δ Y}{Y} = 2 (\frac{Δ d}{d}) + (\frac{Δ l}{l})

(Y + Δ Y) = (2 \pm 0.2) \times 1 0^{11} Nm^{- 2}

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Question Text	A student performs an experiment to determine the Young's modulus of a wire, exactly $2 m$ long, by Searle's method. In a particular reading, the student measures the extension in the length of the wire to be $0.8 mm$ with an uncertainty of $\pm 0.05 mm$ at a load of exactly $1.0 kg$ . The student also measures the diameter of the wire to be $0.4 mm$ with an uncertainty of $\pm 0.01 mm$ . Take $g = 9.8 ms^{- 2}$ (exact). The Young's modulus obtained from the reading is
Updated On	Jan 27, 2023
Topic	Units and Measurements
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 2
Upvotes	197
Avg. Video Duration	11 min

Text solutionVerified

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