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A rubber cord catapult has cross-sectional area $25 \mathrm{~mm}^2$ and initial length of rubber cord is $10 \mathrm{~cm}$ It is stretched to ${ }^{5 \mathrm{~cm}}$ and then released to project a missile of mass $5 \mathrm{gm}$ Taking $Y_{\text {rubber }}=5 \times 10^8 \mathrm{~N} / \mathrm{m}^2$ velocity of projected missile is
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$250 \mathrm{~ms}^{-1}$
Potential energy stored in the rubber cord catapult will be converted into kinetic energy of mass.
$\frac{1}{2} m v^2=\frac{1}{2} \frac{Y A l^2}{L} \Rightarrow v=\sqrt{\frac{Y A l^2}{m L}}$
$=\sqrt{\frac{5 \times 10^8 \times 25 \times 10^{-6} \times\left(5 \times 10^{-2}\right)^2}{5 \times 10^{-3} \times 10 \times 10^{-2}}}=250 \mathrm{~m} / \mathrm{s}$
$\frac{1}{2} m v^2=\frac{1}{2} \frac{Y A l^2}{L} \Rightarrow v=\sqrt{\frac{Y A l^2}{m L}}$
$=\sqrt{\frac{5 \times 10^8 \times 25 \times 10^{-6} \times\left(5 \times 10^{-2}\right)^2}{5 \times 10^{-3} \times 10 \times 10^{-2}}}=250 \mathrm{~m} / \mathrm{s}$
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