An iron bar of length $ℓ$ cm and cross section A $c m^{2}$ is pulled by a force of F dynes from ends so as to produce an elongation $Δ ℓ c m$ . Which of the following statement is correct ?

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Elongation is inversely proportional to length

Elongation is directly proportional to Young’s modulus

Elongation is inversely proportional to A

Elongation is directly proportional to cross section A

answer is C.

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Detailed Solution

According to Hooke’s Law

Stress $α$ strain i.e., $\frac{F}{A} \propto \frac{Δ l}{l}$

$\Rightarrow$ For same $F & ℓ, Δ l \propto \frac{1}{A}$

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