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