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A boy has a catapult made of a rubber co...

A boy has a catapult made of a rubber cord of length `42 cm` and diameter `6.0 mm`. The boy stretches the cord by `20 cm` to catapult a stone of mass `20 g`. The stone flies off with a speed of `20 ms^(-1)`. Find Young's modulus for rubber. Ignore the change in the cross section of the cord in stretching.

Text Solution

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When a catapult is stretched up to length l, the the stored energy in it `=Deltak.E`
`=1/2.((YA)/L)(DeltaI)^(2)=1/2mv^(2)`
`impliesy=(mv^(2)L)/(Delta(DeltaI)^(2))`
m=0.02kg
`v=20ms^(-1)`
`L=0.42m`
`A=(pid^(2))//(4)`
`d=6xx10^(-3)m`
`Deltal=0.2m`
`(0.002xx400xx0.42xx4)/(pixx36xx10^(-6)xx0.04)`
`=2.3xx10^(6)N//m^(2)`
So order is `10^(6)`.
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