JEE Main · 2022 · 25 Jul 2022 · Shift 1 · Elasticity & SHM

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A wire of length L and radius r is clamped rigidly at one end. When the other end of the wire is pulled by a force F, its length increases by 5 cm. Another wire of the same material of length 4L and radius 4r is pulled by a force 4F under same conditions. The increase in length of this wire is ______ cm.

Answer: 5

Solution

The elongation of a wire is given by

Δ ℓ = \frac{F L}{A Y} = \frac{F L}{π r ^{2} Y}

. For the first wire:

Δ ℓ_{1} = \frac{F L}{π r ^{2} Y} = 5

cm. For the second wire with length

4 L

, radius

4 r

, and force

4 F

Δ ℓ_{2} = \frac{4 F \cdot 4 L}{π ( 4 r ) ^{2} Y} = \frac{16 F L}{16 π r ^{2} Y} = \frac{F L}{π r ^{2} Y} = 5

cm.

JEE Main · 2022 · 25 Jul 2022 · Shift 1 · Integer answer

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