Question

If the interatomic spacing in steel wire is $2.8\times {10}^{-10}m$ and $Y_{steel}=2\times {10}^{11}N{m}^{-2}$, then the force constant in N/M is

• A. 56
• B. 5.6
• C. 0.56
• D. 560

Answer 1

The correct option is A

56

Step1: Given data

Interatomic spacing in a steel wire is $2.8\times {10}^{-10}m$

$Y_{steel}=2\times {10}^{11}N{m}^{-2}$

Step2: Interatomic force constant

1. When a solid is subjected to an external force, the distance between its atoms changes, and the interatomic force attempts to restore the original dimension.
2. The interatomic force constant is defined as the ratio of interatomic force to change in interatomic distance.

Step3: Formula used

$F=Y\times r[whereF=interatomicforcecons\tan t,Y=young\text{'}smodulus,r=interatomicdis\tan ce]$

Step4: Calculating force constant

The Young's modulus of steel wire must be entered here.
So we can write $Y_{steel}=2\times {10}^{11}N{m}^{-2}$ instead of Y.

$$\begin{gathered} F=Y\times r \\ F=Y_{steel}\times r \\ F=(2\times {10}^{11})N{m}^{-2}\times (2.8\times {10}^{-10})m \\ F=5.6\times {10}^{11-10}N{m}^{-2+1} \\ F=5.6\times 10N{m}^{-2} \\ F=56N{m}^{-1} \end{gathered}$$

Hence, option A is the correct answer