Question

You have two ropes with different Young’s modulus, but the same area of cross section and length. You apply the same force on both of these. The change in the length is -

A) More for the rope with higher Young’s modulus

B) Less for the rope with higher Young’s modulus

C) Same for both the ropes.

Answer 1

Hi,

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We know that, Change in length is given by:

- Force applied (N).

- Length of the roped (m).

A - Area of cross-section of the rope (m²)

Y -Young's modulus (N/m²)

Here, force, length and Area of cross-section of the two given ropes are same.

Hence, We can say that the change in length is inversely proportional to the Young's modulus:

That is when Young's modulus of the rope increases, the change in length of the rope decreases.

Hence, the change in the length of the rope will be less for the rope with higher Young’s modulus.

So the correct option is (B) Less for the rope with higher Young’s modulus.

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