Question

A wire of length Land radius r is rigidly fixed at one end. On stretching the other end of the wire with a force F the increase in length is l. If another wire of the same material but double the length and radius is stretched with a force 2F, then increase in length is ______.

विकल्प

• `l/4`

• 2l

• `l/2`

• l

Answer 1

A wire of length Land radius r is rigidly fixed at one end. On stretching the other end of the wire with a force F the increase in length is l. If another wire of the same material but double the length and radius is stretched with a force 2F, then increase in length is l.

Explanation:

Let the length of wire = L

Radius = r

When a force Fis applied, then increase in length = (l).

Since, Young's modulus

Y = `("F"/(pi"r"^2))/(l/"L")`

`=> "Y" = "Fl"/(pi "r"^2 l)`    ...(i)

For another wire,

length of wire, L' = 2L

Radius of wire, r' = 2r

Applied force, F' = 2F

`therefore "Y" = ("F'""L'")/(pi"r"^2 l')` where, /'= elongation in length

`= (2"F" * 2"L")/(pi(2"r")^2 * "l'")`

`= (4 "FL")/(4pi"r"^2"l'")`

Y = `"FL"/(pi"r"^2 "l'")`   ...(ii)

From Eqs. (i) and (ii), we have l' = l