TS EAMCET · Physics · Mechanical Properties of Solids

A steel rod has radius $50 mm$ and length $2 m$ . It is stretched along its length with a force of $400 kN$ . This causes an elongation of $0.5 mm$ . Find the (approximate) Young's modulus of steel from this information.

A $2 \times 10^{10} N m^{2}$
B $10^{11} N m^{2}$
C $2 \times 10^{11} N m^{2}$
D $10^{12} N m^{2}$

Verified Solution

Answer & Solution

Correct Answer

(C) $2 \times 10^{11} N m^{2}$

Step-by-step Solution

Detailed explanation

Elongation, ΔL=FALY FA=400×103π50×10-32 ∴A=πr2 -50.92×106 ⇒ Y=50.92×106×20.5×10-3 ∴Y=2×1011Nm2

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.

Same subject

Explore more questions on app

From TS EAMCET

Explore more questions on app

A steel rod has radius 50 mm and length 2 m. It is stretched along its length with a force of 400 kN. This causes an elongation of 0.5 mm. Find the (approximate) Young's modulus of steel from this information.

Step-by-step Solution

A steel rod has radius $50 mm$ and length $2 m$ . It is stretched along its length with a force of $400 kN$ . This causes an elongation of $0.5 mm$ . Find the (approximate) Young's modulus of steel from this information.