Question

Two wires of the same material and length but diameters in ratio $1:2$ are stretched by the same force. The potential energy per unit volume for the two wires when stretched will be in the ratio :-

• A. $16:1$
• B. $4:1$
• C. $2:1$
• D. $1:1$

Answer 1

The correct option is A $16:1$

$U=\frac{1}{2}F\Delta l=\frac{1}{2}F\frac{FL}{YA}=\frac{1}{2}\frac{F^{2}L}{YA}$

same material means they have same bulk modulus and length are also same.

therefore

$d_1:d_2=r_1:r_2=\frac{1}{2}$

$\frac{U_1}{U_2}=\frac{\frac{1}{2}\frac{F^{2}L}{Y\pi r_1^4}}{\frac{1}{2}\frac{F^{2}L}{Y\pi (2r_1{)}^4}}=\frac{16}{1}$