A rubber cord has a cross -sectional area `1 mm^(2)`and total unstretched length`10.0cm`. It is streched to `12.0 cm` and then released to project a missile of mass 5.0 g.Taking young's modulus Y for rubber as `5.0xx10^(8) N//m^(2)`.Calculate the velocity of projection .

Options

A. `20(m)/(s)`
B. `15(m)/(s)`
C. `12(m)/(s)`
D. `6(m)/(s)`

Answer

A

Explanation

Assumption. Total elastic energy of catapult is converted into kinetic energy of missile without any heal loss.
Elastic energy `=(1)/(2)xx`load`xx`extension
here extension,
`triangleL=12.0-10.0=2.0cm=2.0xx10^-2m`
From relation `Y=(FL)/(AtriangleL)`
Load `F=(YAtrianglL)/(L)`
`=(5.0xx10%8xx1xx10^-6xx2.0xx10^-2)/(10.0xx10^-2)=100N`
If v is velocity of projection we have
Elastic energy of catapult`=`kinetic energy of missile
i.e., `(1)/(2)xx`load`xx`extension`=(1)/(2)mv^2`
`(1)/(2)xx100xx2.0xx10^-2=(1)/(2)xx(5.0xx10^-3)v^2`
This gives `v^2=(100xx10^-2xx2)/(5xx10^-3)=400`
`v=sqrt(400)=20(m)/(s)`