A rubber cord catapult has cross sectional area 25 `mm^(2)`'. Initial length of rubber cord is 10 cm. It is stretched by 5 cm and then released to project a stone of mass 5 g. Taking the Young's modulus for rubber to be `5 xx 10 Nm^(-2)` the velocity of the stone is

Options

A. `20 ms^(-1)`
B. `100 ms^(-1)`
C. `250 ms^(-1)`
D. `150 ms^(-1)`

Answer

C

Explanation

`W = (1)/(2) mv^(2) ` kinetic energy of the stone .
But ` W = (1)/(2) ` (stress ) (strain ) (volume )
`= (1)/(2) Y ( "strain")^(2) ("volume ") = (1)/(2) Y ((DeltaL)/(L))^(2) ` (AL) = Elastic Potential energy