A) 360 \[\pi \]N
B) 36 N
C) \[\text{36}\pi \times \text{1}{{0}^{5}}\text{ N}\]
D) \[\text{14471}\times \text{1}{{0}^{\text{3}}}\text{ N}\]
Correct Answer: A
Solution :
The ratio of stress to strain is known as Youngs modulus of wire \[Y=\frac{F/A}{l/L}\] \[\Rightarrow \] \[F=\frac{YAl}{L}\] Given, \[Y=9\times {{10}^{10}}N/{{m}^{2}}\], \[A=\pi {{r}^{2}}=\pi {{(2\times {{10}^{-3}})}^{2}}\], \[l=0.1%L\] \[\therefore \] \[F=\frac{9\times {{10}^{10}}\times \pi \times {{(2\times {{10}^{-3}})}^{2}}\times 0.1}{100}\] \[\Rightarrow \] \[F=360\,\pi \,N\]
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