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# A Mass of 1 Kg is Hung from a Steel Wire If Radius 0.5 Mm and Length 4 M. Calculate the Extension Produced. What Should Be the Area of Cross-section of the Wire So that Elastic Limit is Not Exceeded? Change in Radius is Negligible - Physics

#### Question

A mass of 1 kg is hung from a steel wire if radius 0.5 mm and length 4 m. Calculate the extension produced. What should be the area of cross-section of the wire so that elastic  limit is not exceeded? Change in radius is negligible

(Given : g = 9.8 m/s2; Elastic limit of steel is 2.4 x 108 N/m2;Y for steel (Ysteel) = 20 x 1010 N/m2; π = 3.142)

#### Solution

Given : g = 9.8 m/s2; Elastic limit of steel is 2.4 x 108 N/m2;Y for steel (Ysteel) = 20 x 1010 N/m2; π = 3.142

To find:  Extension in length (l)
Area of cross section (A)
Formulae:

i. Y = FL/Al
ii. Elastic limit = F/A

l=(FL)/(AY)=(MgL)/(pir^2Y)

l=(1xx9.8xx4)/(3.14xx(0.5xx10^-3)^2xx20xx10^10)

l = 2.495x 10-4 m
From formula (ii),

A=(Mg)/("Elastic limit")

=(1xx9.8)/(2.4xx10^8)

A=4.o83xx10^-8 m^2

The extension produced in length is 2.495x 10-4 m and the area of cross section of the wire should be 4.083 x 10-8 m2.

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