A wire can be broken by applying a load of 30 kg-wt. The force required to break the wire of twice the diameter is

Question

A wire can be broken by applying a load of 30 kg-wt. The force required to break the wire of twice the diameter is (A) 240 kg-wt (B) 100 kg-wt (C) 120 kg-wt (D) 150 kg-wt

Tardigrade Admin · Accepted Answer

Breaking Stress =( text Force / text Area ) ∴ wire is same, breaking stress is constant F propto A ∴ (F1/F2)=(A1/A2) =(π D12/4) × (4/π D22)=((D1/D2))2=(1/4) ∴ F2=40 × 30=120 kg wt

Q. A wire can be broken by applying a load of $30 k g - wt$ . The force required to break the wire of twice the diameter is

$240 k g - wt$

$100 k g - wt$

$120 k g - wt$

$150 k g - wt$

Breaking Stress $= \frac{Force}{Area}$
$∴$ wire is same, breaking stress is constant
$F \propto A$
$∴ \frac{F _{1}}{F _{2}} = \frac{A _{1}}{A _{2}} = \frac{π D _{1}^{2}}{4} \times \frac{4}{π D _{2}^{2}} = (\frac{D _{1}}{D _{2}})^{2} = \frac{1}{4}$
$∴ F_{2} = 40 \times 30 = 120 k g wt$

Q. A wire can be broken by applying a load of 30kg−wt. The force required to break the wire of twice the diameter is

240kg−wt

100kg−wt

120kg−wt

150kg−wt