QJEEM23Ph860c: JEE Main 2023 Physics - Class 11 JEEM23Ph860c Solution: A force is applied to a steel wire 'A', rigidly clamped at one…

Question

Verified Solution • 2025–26 Session moderate

A force is applied to a steel wire 'A', rigidly clamped at one end. As a result elongation in the wire is

0.2 \mathrm{~mm}

. If same force is applied to another steel wire '

\mathrm{B}

' of double the length and a diameter

2.4

times that of the wire '

\mathrm{A}

', the elongation in the wire '

\mathrm{B}

' will be (wires having uniform circular cross sections)

Accepted Answer

$∵$ $Δ l = \frac{F l (4)}{Y π d^{2}}$

$\frac{Δ l_{1}}{Δ l_{2}} = \frac{Δ l_{1}}{d_{1}^{2}} \times \frac{d_{2}^{2}}{l_{2}}$

$\frac{0.2}{Δ l_{2}} = \frac{1}{2} \times (2.4)^{2}$

$Δ l_{2} = \frac{2 \times 0.2}{{(2.4)}^{2}}$

$= 6.9 \times 10^{- 2}$ mm

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