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 stretching.

Options

A. `10^(6)Nm^(-2)`
B. `10^(3)Nm^(-2)`
C. `10^(8)Nm^(-2)`
D. `10^(4)Nm^(-2)`

Answer

A

Explanation

When catapult is released, elastic potential energy stored in cord gets converted to KE of stone.
EPE lost by cord = KE gained by stone
`(1)/(2)((YA)/(l))Deltal^(2)=(1)/(2)mV^(2)` `rArrYxx(pi(3xx10^(-3))^(2))/(0.42)xx(0.2)^(2)=0.02xx(20)^(2)rArrY=(0.02xx400xx0.42)/(pixx9xx10^(-6)xx0.04)~~30xx10^(6)`Slunits