Question

A wire of length l area of cross section A and weight W is subjected to external force 2w. If Y is the Young's modulus then total extension in the wire is

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Answer 1

Answer:

Work done = 12×12× stress ×× strain ×× volume

=12=12×Y×(strain)2×Volume×Y×(strain)2×Volume

=12=12×Y×(xL)2×Y×(xL)2×AL×AL

=Yx2A2L=Yx2A2L

Hence b is the correct answer.

Answer 2

Answer:

The total extension in the wire is $\dfrac{2Wl}{AY}$

Explanation:

Given that,

Length = l

External force = 2 W

Area of cross section = A

We need to calculate the total extension in the wire

Using formula of young modulus

$Y=\dfrac{\dfrac{F}{A}}{\dfrac{\Delta l}{l}}$

Where, A = area

F = force

L = length

Put the value into the formula

$Y=\dfrac{2Wl}{A\Delta l}$

$\Delta l=\dfrac{2Wl}{AY}$

Hence, The total extension in the wire is $\dfrac{2Wl}{AY}$