Question

Two wires of the same material and same mass are stretched by the same force. Their length are in the ratio $2:3$. Their elongations are in the ratio

• A. $3:2$
• B. $2:3$
• C. $4:9$
• D. $9:4$

Answer 1

The correct option is C $4:9$

Let the lengths of the two wires be $2l$ and $3l$.
Two materials have same mass.
Thus we get $\rho \left(2l\right)A_1=\rho \left(3l\right)A_2$
Thus $2A_1=3A_2$
Now their elongations are given as $\Delta l_1=\frac{F2l}{A_{1}Y}$ and $\Delta l_2=\frac{F3l}{A_{2}Y}$
Thus we get $\frac{\Delta l_1}{\Delta l_2}=\frac{4}{9}$