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:

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

B $\frac{MgL}{AL_1}$

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

D $\frac{MgL_1}{AL}$

The answer is C.

Solution

Stress $= \frac{Mg}{A}$ ; strain $= \frac{\Delta L}{L} = \frac{L_1 - L}{L}$ Young's modulus $Y = \frac{stress}{strain} = \frac{MgL}{A(L_1 - L)}$

Concept expression for Young's modulus

15 questions from this chapter have appeared across 11 exam years.