A stone of mass $20\, {g}$ is projected from a rubber catapult of length $0.1\, {m}$ and area of cross section $10^{-6} \,{m}^{2}$ stretched by an amount $0.04\, {m}$. The velocity of the projected stone is $....\,m\,/s.$ (Young's modulus of rubber $=0.5 \times 10^{9}\, {N} / {m}^{2}$ )
JEE MAIN 2021, Medium
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$\frac{1}{2} \cdot k \cdot x ^{2}=\frac{1}{2} \cdot \frac{ YA }{ L }\cdot x ^{2}$
By energy conservation
$\frac{1}{2} \cdot \frac{ YA }{ L } \cdot x ^{2}=\frac{1}{2} mv ^{2}$
$\frac{0.5 \times 10^{9} \times 10^{-6} \times(0.04)^{2}}{0.1}=\frac{20}{1000} v ^{2}$
$\therefore \quad v ^{2}=400$
$ v =20 m / s$
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