MHT CET · Physics · Mechanical Properties of Solids

A force of \(10 \mathrm{~N}\) is required to break a wire of radius \(1 \mathrm{~mm}\). The force required to break the wire of same material, but radius \(3 \mathrm{~mm}\) will be

A \(\frac{10}{9} \mathrm{~N}\)
B \(\frac{10}{3} \mathrm{~N}\)
C \(90 \mathrm{~N}\)
D \(30 \mathrm{~N}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(90 \mathrm{~N}\)

Step-by-step Solution

Detailed explanation

We know that, the required force depends upon the cross-sectional area. \(F=\) Stress \(\times\) Area
So, \(\frac{F_{1}}{F_{2}}=\frac{R_{1}^{2}}{R_{2}^{2}}\)
\(\Rightarrow F_{2}=\frac{3^{2}}{1^{2}} \times 10=90 \mathrm{~N}\)

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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