Question

Steel ruptures when a shear of $3.5\times {10}^{8}N{m}^{-2}$ is applied. The force needed to punch a $1cm$ diameter hole in a steel sheet $0.3cm$ thick is nearly

• A. $1.4\times {10}^{4}N$
• B. $2.7\times {10}^{4}N$
• C. $3.3\times {10}^{4}N$
• D. $1.1\times {10}^{4}N$

Answer 1

The correct option is C $3.3\times {10}^{4}N$

Shear is the horizontal stress on the sheet mathematically given by $\frac{F}{A}$ where F is applied perpendicular to the area A.

In our case, the area A would be circumference of the hole $\pi \times diameter$ times the thickness of the sheet.

From the question, shear stress $=3.5\times {10}^{8}N{m}^{-2}=\frac{F}{\pi \times 1\times {10}^{-2}m\times 0.3\times {10}^{-2}m}$

$⟹F=3.3\times {10}^{4}N$