Question

A steel and a brass wire each of length 50cm and cross-sectional area 0.005cm^2 hang from a ceiling and are 15 apart . Lower ends of the wires are attached to a light horizontal bar. A suitable downward load is applied to the bar so that each of the wires extends in length by 0.1 cm. At what distance from the steel wire the load must be applied?

Answer 1

Answer:

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Answer 2

Given:-

The Length of each steel and Brass wire is$=50\ cm$

Area of cross-section$=0.005\ cm^{2}$

The distance between the wires is$=15 cm$

Extension of the wire is$=0.1\ cm$

Young's modulus of steel $(Y_{s})$$=2\times1012\ dynes/cm^{2}$

Young's modulus of a brass $(Y_{b} )$$=1\times1012 \ dynes/cm^{2}$

To Find:

Distance from the steel wire at which load is applied

Solution:

We know that Young's modulus is given by

$Y=\dfrac{stress}{strain}$

$Stress=\dfrac{force}{area}$

$Strain=\dfrac{Change\ in\ the\ length}{original\ length }$

$Y=\dfrac{F/A}{\Delta l/l}$

⇒ $F=\dfrac{YA\Delta l}{l}$

∵ A, ∆l, and l are all same for both the wires.

moments about point A

$F_{s}(x)=F_{b}(15-x)$

$Y_{s}(x)=Y_{b}(15-x)$

 Put values of $Y_{s}\ and \ Y_{b}$

$2\times1012(x)=(1\times1012)(15-x)\\2x=(15-x)$

$3x=15\\x=5.$

Distance from the steel wire is $5 \ cm.$