Question

a steel wire is loaded by 2kg. If the radius of wire is halved uniformly the length becomes.plzz expail the solution...

A. Double
B. Half
C. Same
D. Four times​

Answer 1

A steel wire is loaded by 2 Kg. If the radius of wire is halved uniformly, the length becomes four times.

here the steel wire's radius has changed because of loading. it is obvious that the volume of wire will remain same because only the shape of wire changes not its quantity.

    let initial length and radius of wire are l and r respectively.

so the volume of wire = πr²l ...(1)

now the radius of wire is halved uniformly.

∴ new radius of wire = r/2

let the length of wire is l'

∴  the volume of wire = π(r/2)²l' = πr²l'/4

from equation (1), we get

⇒ πr²l = πr²l'/4

⇒ 4l = l'

hence, it is clear that the length of wire becomes four times of its initial. so option (D) is correct.