Question

A cylindrical metallic wire is stretched to double its length. Which of the following will NOT change for the wire after stretching?

Options

• Its curved surface area.

• Its total surface area.

• Its volume.

• Its radius.

Answer 1

Its volume.

Explanation:

Let initial length = L and radius = r.

Volume V = πr²L depends only on the material, so when the wire is stretched to length 2L.

The volume remains the same

πr²L = πr'² × 2L 

⇒ `r'^2 = r^2/2`

So, volume does not change.

Radius changes `(r' = r/sqrt(2))`, so (d) is wrong.

Curved (lateral) surface = 2πrL

⇒ After stretching becomes `2π(r/sqrt(2)) xx (2L) = 2πrL xx sqrt(2)` .

So, it changes a is wrong.

Total surface includes the end areas 2πr² which also change because r changes, so total surface area changes b is wrong.