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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 streching.

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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Knowledge Check

  • A rubber cord has a cross-sectional area 10^(-6) m^(2) and total unstretched length 0.1 m. It is stretched to 0.125 m and then released to project a particle of mass 5.0 g. The velocity of projection is [Given, Young’s modulus of rubber Y = 5 xx 10^(8) N//m^(2) ]

    A
    45 m/s
    B
    30 m/s
    C
    25 m/s
    D
    15 m/s