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A mass of 1kg is attached to the end of a rubber string 25cm long having radius 2mm,which is rotating in horizontal plane in a radius of 28cm with 50rpm.What is young modulus of string in $N/m^2$

$\begin{array}{1 1}(A)\;2\times 10^6\\(B)\;3\times 10^6\\(C)\;4\times 10^6\\(D)\;5\times 10^6\end{array} $

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Force applied by mass =$m\omega^2R$
$\Rightarrow 1\times (\large\frac{50\times 2\pi}{360})^2$$\times .28$
$\Rightarrow \large\frac{25\times \pi^2\times .28}{9}$
Extension $=\Delta l=R-l$
$\Rightarrow (28-25)$cm
$\Rightarrow 3$cm
Area $=\pi r^2$
$\Rightarrow \pi(2\times 10^{-3})^2$
$\Rightarrow 4\pi \times 10^{-6}m^2$
As we know
$Y=(\large\frac{f}{a})\times \frac{l}{\Delta l}$
$\;\;\;=\large\frac{25\pi^2\times .28}{9\times 4\pi \times 10^{-6}}\times \frac{25}{3}$
$\;\;\;=\large\frac{625\pi\times .07\times 10^6}{27}$
$\;\;\;=5.09\times 10^6N/m^2\approx 5\times 10^6 N/m^2$
Hence (D) is the correct answer.
answered May 7, 2014 by sreemathi.v

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