Question

How much force is required to produce an increase of 0.2% in the length of a brass wire of diameter 0.6 mm? [Young's modulus for brass = $0.9\times {10}^{11}$ $N/m^2$]

• A. Nearly 17 N
• B. Nearly 34 N
• C. Nearly 51 N
• D. Nearly 78 N

Answer 1

The correct option is C Nearly 51 N

Given,

Strain, $\frac{\Delta L}{L}=\frac{0.2}{100}$

Stress = Young modulus x strain

$F=AY\frac{\Delta L}{L}$

$F=\frac{\pi {(0.6\times {10}^{-3})}^2}{4}(0.9\times {10}^{11})\times \frac{0.2}{100}$

$F=\frac{81\pi }{5}N=50.89N$

Hence, required force is nearly $51N$