Question

Under the same load, wire A having length $50 m$ and cross section $25 \times 10^{-5} m ^2$ stretches uniformly by the same amount as another wire $B$ of length $60 m$ and a cross section of $30 \times 10^{-5}$ $m ^2$ stretches The ratio of the Young's modulus of wire $A$ to that of wire $B$ will be :

• A. $1: 4$
• B. $1: 1$
• C. $3=10$
• D. $1: 2$

Hint:

Young's modulus is inversely proportional to the product of the length and cross-sectional area for equal strain.

Answer 1

The Correct Option is B

The formula for Young's modulus is given by: \[ Y = \frac{F \times L}{A \times \Delta L} \] where \( F \) is the force, \( L \) is the length, \( A \) is the cross-sectional area, and \( \Delta L \) is the elongation. Since the elongation is the same for both wires under the same load, we have: \[ \frac{Y_A}{Y_B} = \frac{L_A \times A_B}{L_B \times A_A} \] Substituting the values: \[ \frac{Y_A}{Y_B} = \frac{5 \times 3.0 \times 10^{-5}}{6.0 \times 2.5 \times 10^{-5}} = 1 \] Thus, the ratio is 1:1.