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A boy has a catapult made of a rubber co...

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.

A

`10^Nm^(-2)`

B

`10^3Nm^(-2)`

C

`10^8Nm^(-2)`

D

`10^4Nm^(-2)`

Text Solution

Verified by Experts

The correct Answer is:
A
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=1/2mv^2`
`impliesYxx(pi(3xx10^(-3))^(2))/(0.42)xx(0.2)=0.02xx(20)^2impliesY=(0.02xx400xx0.42)/(pixx9xx10^(-6)xx0.04)~~3xx10^6` SI units
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