Verified Solution • 2025–26 Session moderate

QJEEM22Pha392: JEE Main 2022 Physics - Class 11 JEEM22Pha392 Solution: A wire of length and radius is clamped rigidly at one end. When …

A wire of length L\mathrm{L} and radius r\mathrm{r} is clamped rigidly at one end. When the other end of the wire is pulled by a force F\mathrm{F} , its length increases by 5 cm5 \mathrm{~cm} . Another wire of the same material of length 4L4 \mathrm{L} and radius 4r4 \mathrm{r} is pulled by a force 4F4 \mathrm{F} under same conditions. The increase in length of this wire is __________________ cm\mathrm{cm} .

Step-by-Step Verified Solution

F/AΔL/L=Y{{F/A} \over {\Delta L/L}} = Y

⇒ΔL=FLAY\Rightarrow \Delta L = {{FL} \over {AY}}

ΔL2ΔL1=(F2F1)×(L2L1)×(A1A2){{\Delta {L_2}} \over {\Delta {L_1}}} = \left( {{{{F_2}} \over {{F_1}}}} \right) \times \left( {{{{L_2}} \over {{L_1}}}} \right) \times \left( {{{{A_1}} \over {{A_2}}}} \right)

=4×4×116=1= 4 \times 4 \times {1 \over {16}} = 1

ΔL2=ΔL1=5\Delta {L_2} = \Delta {L_1} = 5 cm.

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