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Question

A cable breaks if stretched by more than 2mm. It is cut into two equal parts. How much either part can be stretched without breaking?


A

0.25m

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B

0.5mm

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C

1mm

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D

2mm

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Solution

The correct option is C

1mm


Step 1: Given

Maximum elongation in the original cable, L1=2mm

The original length of the cable L

Length of the cables after breaking L2

Step 2: Hooke's law

Hooke's law states that the deformation of a body is directly proportional to the applied load.

L=PLAE

(Where L is the deformation, P,L,A,E are the applied load, the length, the area, and Young's modulus respectively.)

Step 3: Determine the relationship between the lengths and the deformations

Form the above formula, LL

From the above proportionality, we can write

L1L2L1L2

Step 4: Calculate the maximum deformation

Let the deformation after breaking be L2

L1L2=L1L22L2=LL2L2=1mm

Therefore, option C is the correct option.


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