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 $2m/s$. Find the elongation of the wire when the block is at the bottom of the circle. Young’s modulus of the material of the wire $=2.0\times {10}^{11}N/m^2$.

• A. $0.002cm$
• B. $0.003cm$
• C. $0.001cm$
• D. $0.004cm$

Answer 1

The correct option is C $0.001cm$


$W=10N,m=1kg,A=3\times {10}^{-6}{m}^{2}R=l=0.2m,V=2m{s}^{-1},Y=2\times {10}^{11},\Delta l=?$
$\Delta l=\frac{\text{Stress}\times l}{Y}$
$T-W=\frac{m\times v^2}{R}$
$T=W+\frac{m\times v^2}{R}$
$T=10+\frac{1\times 2^2}{0.2}$
$T=30N$
$\Delta l=\frac{T\times l}{A\times Y}$
$\Delta l=\frac{30\times 0.2}{3\times {10}^{-6}\times 2\times {10}^{11}}$
$\Delta l={10}^{-5}m$