Question

A wire can be broken by applying a load of 20 kg wt. The force required to break the wire of twice
the diameter is :

• A. 20 kg wt
• B. 5 kg wt
• C. 80 kg wt
• D. 160 kg wt.

Answer 1

The correct option is C 80 kg wt

Breaking stress is the characteristic of the material. Hence, for two wires of same material having different thickness

$\frac{F_1}{r_1^2}=\frac{F_2}{r_2^2}$

$\frac{F_1}{r^2}=\frac{F_2}{(2r{)}^2}$

$\frac{20}{r^2}=\frac{F_2}{\left(4r^2\right)}$

So, $F_2=80kgwt$