Question

Work done in stretching a wire through 1 mm is 2 J. What amount of work will be done for elongating another wire of same material, with half the length and double the radius of cross-section, by 1 mm?

पर्याय

• 2 J

• 4 J

• 8 J

• 16 J

Answer 1

16 J

Explanation:

Given that, work done, W = 2J

As, we have two wires of same material and they are elongated to the same length.

So, this means, their Young's modulus (Y) is same and Δl₁ = Δl₂ = Δl (say)

The work done in stretching a wire,

W = `1/2 "F" Delta "l"`

Now, for both the wires we have

`"W"_1/"W"_2 = (1/2 "F"_1 Delta"l")/(1/2 "F"_2 Delta"l")`

`=> "W"_2 = 2 xx "F"_2/"F"_1`   ....(i)

The forces by which the wires are stretched can be expressed as the ratio,

`"F"_1/"F"_2 = ("YA"_1 (Delta l)/"L"_1)/("YA"_2 (Delta l)/"L"_2)`

`= ("r"_1^2 "L"_2)/("r"_2^2 "L"_1)`    ....(iii)

Given, r₂ = 2r₁ and L₂ = `"L"_1/2`

Now, substituting the given values in Eq. (ii), we get

`"F"_1/"F"_2 = ("r"_1^2 "L"_1)/(4 "r"_1^2 2 "L"_2) = 1/8`   ...(iii)

From Eqs. (i) and (iii), we get

W₂ = 2 × 8

= 16 J