Solved: PHYSICS Question for NEET

NEET PHYSICSEasy

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:

$\frac{Mg(L_1 - L)}{AL}$

$\frac{MgL}{AL_1}$

$\frac{MgL}{A(L_1 - L)}$

$\frac{MgL_1}{AL}$

Step-by-Step Solution

Definition of Young's Modulus ( $Y$ ): Young's modulus is defined as the ratio of longitudinal stress ( $\sigma$ ) to longitudinal strain ( $\varepsilon$ ) within the elastic limit. $Y = \frac{\sigma}{\varepsilon}$
Longitudinal Stress ( $\sigma$ ): Stress is the restoring force per unit area. Here, the force ( $F$ ) is the weight of the suspended mass $M$ . $F = Mg$ $\sigma = \frac{F}{A} = \frac{Mg}{A}$
Longitudinal Strain ( $\varepsilon$ ): Strain is the ratio of the change in length ( $\Delta L$ ) to the original length ( $L$ ). Original Length = $L$ Final Length = $L_1$ Change in Length ( $\Delta L$ ) = $L_1 - L$ $\varepsilon = \frac{\Delta L}{L} = \frac{L_1 - L}{L}$
Substitution: Substituting the values of stress and strain into the Young's modulus formula: $Y = \frac{\frac{Mg}{A}}{\frac{L_1 - L}{L}}$ $Y = \frac{Mg}{A} \times \frac{L}{L_1 - L} = \frac{MgL}{A(L_1 - L)}$

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