An Indian rubber cord L metre long and area of cross-section A `"metre"^(2)` is suspended vertically. Density of rubber is D `"kg/metre"^(2)`. If the wire extends by `l` metre under its own weight, then extension `l` is

Options

A. `(L^(2)Dg)/(2E)`
B. `(L^(2)Dg)/(E)`
C. `(L^(2)Dg)/(4E)`
D. L

Answer

A

Explanation

(a) Volume of the rubber cord=AL
Weight of the rubber cord =ALDg.
`therefore` Stress`=(ALDg)/(A)=LDg`
The weight of the rubber cord acts at the centre of gravity which is `(L)/(2)` from the top.
`therefore` Strain `=(l)/(L//2)=(2l)/(L)`
So, Young's modulus, E`=("Stress")/("Strain")=(LDg)/(2l//L)=(L^(2)Dg)/(2l)`
or `l=(L^(2)Dg)/(2E)`