Question

1. A wire 200 cm long and 1 mm in diameter
long and 1 mm in diameter when stretched by a mass of 2 kg increases in
length by 0.24 mm. Calculate the stress, the strain and round
ulate the stress, the strain and Young's modulus. Take g = 9.8 m/s2
Ans: 2.496 x 107 N/m2: 0.12 x 10-3: 2.081 x 1011 N/m​

Answer 1

Answer:STRESS= 24.96×10⁻⁶N/m²

STRAIN=0.00012

YOUNG'S MODULUS=0.208ML⁻¹T⁻²

Explanation:

As we know, the formula of stress is FORCE/AREA

To calculate force, F=mg

Given,

m=2kg

g=9.8m/

Thus, force= 2× 9.8

=19.6N

Given, the diameter of wire=1mm=1×10⁻³

thus, radius=0.5×10⁻⁷

Thus, area=pi r²

=3.14*0.25×10⁻⁶

Thus, stress= force/area

=19.6/0.785×10⁻6

=24.96×10⁻⁶N/m²

The formula of strain is

Strain= Change in length/Original length

=Δx/x

=0.24mm/2000mm

=0.00012

The formula of Young's Modulus=Stress/strain

As calculated above,

Y=24.96×10⁻⁶/0.00012

=0.208ML⁻¹T⁻²

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