MHT CET · Physics · Mechanical Properties of Solids

The ratio of length of two wires of same material is \(1: 2\) and the ratio of their radii
is \(1: \sqrt{2}\). If they are stretched by the same force, the ratio of increase in their
lengths is

A \(\sqrt{2}: 2\)
B \(1: 1\)
C \(2: \sqrt{2}\)
D \(1: 2\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(1: 1\)

Step-by-step Solution

Detailed explanation

\(Y=\frac{F l}{\pi r^{2} \Delta l}\) or \(\Delta l=\frac{F l}{\pi r^{2} Y}\)
\(\Delta l \propto \frac{l}{r^{2}}, \quad \Delta l^{\prime} \propto \frac{2 l}{(\sqrt{2} r)^{2}}\) or \(\Delta l^{\prime} \propto \frac{l}{r^{2}}\)
\(\therefore \frac{\Delta l}{\Delta l^{\prime}}=1\)

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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The ratio of length of two wires of same material is \(1: 2\) and the ratio of their radiiis \(1: \sqrt{2}\). If they are stretched by the same force, the ratio of increase in theirlengths is

Step-by-step Solution

The ratio of length of two wires of same material is \(1: 2\) and the ratio of their radii
is \(1: \sqrt{2}\). If they are stretched by the same force, the ratio of increase in their
lengths is