TS EAMCET · Physics · Mechanical Properties of Solids

The Young's modulus of a material is \(2 \times 10^{11} \mathrm{~N} / \mathrm{m}^2\) and its elastic limit is \(1 \times 10^8 \mathrm{~N} / \mathrm{m}^2\). For a wire of \(1 \mathrm{~m}\) length of this material, the maximum elongation achievable is

A \(0.2 \mathrm{~mm}\)
B \(0.3 \mathrm{~mm}\)
C \(0.4 \mathrm{~mm}\)
D \(0.5 \mathrm{~mm}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(0.5 \mathrm{~mm}\)

Step-by-step Solution

Detailed explanation

Given, Young's modulus of material \(=2 \times 10^{11} \mathrm{~N} / \mathrm{m}^2\) Elastic limit or stress \(=1 \times 10^\theta \mathrm{N} / \mathrm{m}^2\) Length of the wire \(=1 \mathrm{~m}\) We know that,…

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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Column I		Column II
A)	For ring	I)	$\frac{M g \sin θ}{2.5}$
B)	For solid sphere	II)	$\frac{M g \sin θ}{3}$
C)	For solid cylinder	III)	$\frac{M g \sin θ}{3.5}$
D)	For hallow cylinder	IV)	$\frac{M g \sin θ}{2}$