Question

A block of weight $10N$ is fastened to one end of a wire of cross-sectional area $3m{m}^2$ and is rotated in a vertical circle of radius $20cm$. The speed of the block at the bottom of the circle is $2m{s}^{-1}$. If the Young modulus of the material of the wire is $2\times {10}^{11}N{m}^{-2}$, what is the elongation of the wire when the block is at the bottom of the circle?

• A. ${10}^{-4}cm$
• B. ${10}^{-3}cm$
• C. $2\times {10}^{-3}cm$
• D. $2\times {10}^{-4}cm$

Answer 1

The correct option is B

${10}^{-3}cm$

Tension at the lowermost point, $T=W+\frac{m{v}^2}{r}=10+\frac{1\times 2^2}{0.2}=30N$
Now, $Y=\frac{\sigma }{ϵ}=\frac{\left(\frac{T}{A}\right)}{\left(\frac{l}{L}\right)}\Rightarrow l=\frac{TL}{AY}=\frac{30\times 20}{3\times {10}^{-6}\times 2\times {10}^{11}}cm={10}^{-3}cm$