Question

By applying force on an uniform metallic wire its length the wire is extended four times its length with uniform width. Then:

1. The volume of metal in both the cases is same.
2. The surface area of solid wires in both the cases is same.

Which of above statements is/are true?

Options

• only 1

• only 2

• both 1 and 2

• neither 1 nor 2

Answer 1

only 1

Explanation:

On transforming a solid from one shape to another by any external force, the volume of solid remains same.

Let initial length of wire be l and radius be r.

After extension,

Length of wire = 4l and Radius be R.

Since, volume is equal in both the cases:

∴ πr²h = πR²H

⇒ πr²l = πR². 4l

⇒ r² = 4R²

⇒ r = `sqrt(4R^2)`

⇒ r = 2R

⇒ R = `r/2`

Surface area in first case:

⇒ 2πrh

⇒ 2πrl

Surface area in second case:

⇒ 2πRh

⇒ `2π×r/2×4l`

⇒ 4πrl

∴ Surface area of solid wires in both the cases are different.