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 .

Answer

`100 N ; 20 ms^(-1)`

Explanation

Here, `Delta l = 12 - 10 = 2cm =0.02m,`
`l = 10 cm = 0.1 m , A= 1mm^2 = 10^(-6)m^2 ,`
`Y = 5xx10^8 N//m^2`
As, `Y = (F)/(A)xx(l)/(Delta l)` so tension, `F = (Y A Delta l)/(l)`
` =(5xx10^8 xx 10^(-6)xx0.02)/(0.1) = 100 N`
Kinetic energy of missile = elastic potential energy
`(1)/(2)m upsilon^2 = (1)/(2) xx tension xx extension`
or `upsilon = sqrt((tension xx extension)/(m)) = sqrt((100 xx 0.02)/(5//1000))`
` =20 ms^(-1)`