Question

A force F is needed to break a copper wire having radius R The force needed to break a copper wire of radius 2R will be

[assume F is applied along the wire and the wire obeys Hooke's law until it breakes]

• A. F/2
• B. 2 F
• C. 4 F
• D. F/4

Answer 1

The correct option is C 4 F

$F=\frac{YA\Delta l}{l}$

Force $\propto$ area

$F\propto \pi r^2$

$F_1\propto \pi R^2$

$F_2\propto \pi (2R{)}^2=\pi \times 4R^2$

$\frac{F_1}{F_2}=\frac{\pi \times R^2}{\pi \times 4R^2}$

$\frac{F_1}{F_2}=\frac{1}{4}$

$F_2=4F_1$

Hence the correct option is (C).