A wire of length , area of cross section is hanging from a fixed support. The length of the wire changes to when mass is suspended from its free end. The expression for Young’s modulus is [2020]

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Solution

Q.
A wire of length $L$ , area of cross section $A$ is hanging from a fixed support. The length of the wire changes to $L_{1}$ when mass $M$ is suspended from its free end. The expression for Young’s modulus is [2020]

1 $\frac{M g L_{1}}{A L}$

2 $\frac{M g (L_{1} - L)}{A L}$

3 $\frac{M g L}{A L_{1}}$

4 $\frac{M g L}{A (L_{1} - L)}$

Ans.
(4)

Given : initial length = L, area of cross section = A

New length after mass M is suspended on the wire = L

$∴$ Change in length, $Δ L = L_{1} - L .$

Now Young's modulus, $Y = \frac{Stress}{Strain} = \frac{F}{A} \times \frac{L}{Δ L}$

$= \frac{m g}{A} \frac{L}{Δ L} or \frac{M g L}{A (L_{1} - L)}$

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