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A steel sheet fails under a shear stress of 3.5 × 10⁸ N m⁻². The approximate force required to punch a circular hole of diameter 1 cm through a steel plate 0.3 cm thick is:

1. 1.4 × 10⁴ N
2. 2.7 × 10⁴ N
3. 3.3 × 10⁴ N
4. 1.1 × 10⁴ N

Correct answer: 3.3 × 10⁴ N

Solution

The hole is punched by shearing the cylindrical surface of area pi*d*t. F = stress x area = 3.5e8 x pi x 0.01 x 0.003 ~ 3.3e4 N.

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