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 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 68 N

Answer 1

The correct option is C Nearly 51 N

$Y=\frac{F/A}{\frac{\Delta l}{l}}$ $F=\frac{YA\Delta l}{l}$

$F=Y.\pi r^2\frac{\Delta l}{l}$

$F=0.9\times {10}^{11}\times 3.14\times {(\frac{0.6}{2}\times {10}^{-3})}^2\times \frac{0.2}{100}$

$F=0.9\times {10}^{11}\times 3.14\times \times 0.09\times {10}^{-6}\times 2\times {10}^{-3}$

$F=51N$