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A wire of length Land radius r is fixed at one end. When a stretching force F is applied at free end, the elongation in the wire is l. When another wire of same material but of length 2L and radius 2r is also fixed at one end is stretched by a force 2F applied at free end, the elongation in the second wire will be?


A

l4

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B

2l

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C

l

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D

l2

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Solution

The correct option is C

l


The explanation for the correct answer:

Step 1: Given data

Stretching force F

Length 2L

Radius 2r

Step 2: Concept used

Y=FLAΔL

Where,

F is the applied force(N)

L is the initial length(m)

A is the area(m2)

Y is young's modulus(Pa)

Step 3: Calculation

The Young's modulus of a material is calculated as follows:

Young's modulus is unchanged in the second scenario.

Hence,

Y=FLAΔL=2F×2Lπ(2r)2×ΔL=FLπr2ΔL

From the above formula ΔL=l

Therefore, a correct answer is an option(C).


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