The Young's modulus of a rubber string of length 12 cm and density 1.5 kg m-3 is 5×108 N m-2. When this string is suspended vertically, the increase in its length due to its own weight is (take g=10 m s-2)

AP EAMCET · PHYSICS · Mechanical Properties of Solids

The Young's modulus of a rubber string of length $12 cm$ and density $1.5 kg m^{- 3}$ is $5 \times 10^{8} N m^{- 2}$ . When this string is suspended vertically, the increase in its length due to its own weight is (take $g = 10 m s^{- 2}$ )

A $2.16 \times 10^{- 10} m$
B $9.6 \times 10^{- 11} m$
C $9.6 \times 10^{- 3} m$
D $2.16 \times 10^{- 3} m$

Verified Solution

Answer & Solution

Correct Answer

(A) $2.16 \times 10^{- 10} m$

Step-by-step Solution

Detailed explanation

Hooke's law for elasticity, σ=γε γ=σε=FAl∆l here, l is the length of string undergone through tension. Here, the string is suspended vertically and the string is elongated due to its own weight therefore, weight is acting at 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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