A rubber cord catapult has cross-sectional area `25 mm^(2)` and initial length of rubber cord is `10 cm`. It is stretched to `5 cm`. And then released to protect a missle of mass `5 gm` Taking `Y_("nibber")=5xx10^(7)N//m^(2)` velocity of projected missle is

Options

A. ` 20 ms^(-1)`
B. `100 ms^(-1)`
C. ` 250 ms^(-1)`
D. ` 200 ms^(-1)`

Answer

C

Explanation

(c) Elastic potential energy stored in the catapult
`(U=(1)/(2)FDeltaL=(1)/(2)(YA)/(L)DeltaL^(2))` is converted into the kinetic energy of the projectile `(K=(1)/(2)mv^(2))implies v=sqrt((YADeltaL^(2))/(Lm))`
`=[((5xx10^(8))xx(25xx10^(-6))xx(5xx 10^(-2))^(2))/((10xx10^(-2))xx(5xx10^(-3)))]^(1//2)=250 ms^(-1)`