સ્ટીલ પર જ્યારે \(3 .5 \times 10^8\,\,N\,m^{-2}\) જેટલુ આકાર પ્રતિબળ લગાવવામાં આવે ત્યારે તે તૂટે છે.તો \(0.3\,cm\) જાડાઈના સ્ટીલના પતરામાં \(1\,cm\) વ્યાસ વાળો હૉલ કરવા માટે કેટલા બળની જરૂર પડે?

A \(1.4\,\times 10^4\,N\)
B \(2.7\,\times 10^4\,N\)
C \(3.3\,\times 10^4\,N\)
D \(1.1\,\times 10^4\,N\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(3.3\,\times 10^4\,N\)

Step-by-step Solution

Detailed explanation

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…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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