Steel ruptures when a shear of $3 .5 \times 10^8\,\,N\,m^{-2}$ is applied. The force needed to punch a $1\,cm$ diameter hole in a steel sheet $0.3\,cm$ thick is nearly
JEE MAIN 2014, Diffcult
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Shearing strain is created along the side surface of the punched disk. Note that the forces exerted on the disk are exerted along 

the circum ference of the disk, and the total force exerted on its center only.

Letus assume that the shearing stress along the side surface of the disk is uniform, then

$F > \int\limits_{Surface} {d{F_{\max }} = \int\limits_{surface} {{\sigma _{\max }}dA = {\sigma _{\max }}} \int\limits_{surface} {dA} } $

$ = \int {{\sigma _{\max }}} .A = {\sigma _{\max }}.2\pi \left( {\frac{D}{2}} \right)h$

$ = 3.5 \times {10^8} \times \left( {\frac{1}{2} \times {{10}^{ - 2}}} \right) \times 0.3 \times {10^{ - 2}} \times 2\pi $

$ = 3.297 \times {10^4} = 3.3 \times {10^4}N$

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