Question

Two wires are made of the same material and have the same volume. The first wire has cross-sectional area A and the second wire has cross-sectional area $3$A. If the length of the first wire is increased by $\Delta$l on applying a force F, how much force is needed to stretch the second wire by the same amount?

• A. $4$F
• B. $9$F
• C. F
• D. $6$F

Answer 1

Answer: (B)

$9$F

L, v, same

From Hooke’s law

$\frac{F}{A}=4\frac{\Delta l}{L}$ $v_1=v_2$

$F=y\frac{A\Delta l}{L}$ $A\times l=3A\times l_1$ $\Rightarrow l_1=l_{/3}$

$\Rightarrow \frac{F}{F_1}=\frac{\frac{A\Delta l}{l}}{\frac{3A\Delta l}{l_{/3}}}$ $\Rightarrow F_1=9F$

Option (2).