Question

The force required to punch a square hole 2 cm side in steel sheet 2 mm thick is:-
(shearing stress of steel sheet $=3.5\times {10}^{8}N/m^2)$

• A. $5.6\times {10}^{4}N$
• B. $3.4\times {10}^{4}N$
• C. $9.1\times {10}^{4}N$
• D. $6.8\times {10}^{4}N$

Answer 1

The correct option is A $5.6\times {10}^{4}N$

$\begin{array}{c}\text{Breaking area}=2\pi r\times L\\ =2\pi x\\ \text{Breaking area = (Side length)}\times \text{(thickness)}\times 4\\ =2\times {10}^{-2}\times 2\times {10}^{-3}\times 4\\ =4\times {10}^{-5}\times 4\\ =16\times {10}^{-5}\end{array}$

$\begin{array}{cc}F& =\left(\text{Breaking stress}\right)\times \text{Area}\\ & =16\times {10}^{-5}\times 3.5\times {10}^8\\ F& =5.6\times {10}^{4}N\end{array}$