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A boy's catapult is made of rubber cord ...

A boy's catapult is made of rubber cord which is `42cm` long, with `6mm` diameter of cross-section and of negligible mass. The boy keeps a stone weighing `0.02kg` on it and stretches the cond by `20cm` by applying a constant force. When released. The stone flies off with a velocity of `20ms^(-1)`. Neglect the change in the area of cross-section of the cord while stretched. The Young's modulus of rubber is closet to:

Text Solution

Verified by Experts

The potential energy stored in the cord due to stretcing is converted into the kinetc energy of the stone.
`1/2F/_\l=1/2mv^(2)implies` force `F=(mv^(2))/(/_\l)`
Strain`=(/_\l)/l`
Young's modlus `=("Stress")/("Strain")=((F/A))/(/_\l//l)=(mv^(2)//(/_\l))/(pir^(2)((/_\l)/l))`
`=2.97x10^(6)N//m^(2)`
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