Question

The following four wires of length L and radius R are made of the same material which of these will have the largest extension when the when the same tension is applied ?(A)200 CM,r 0.2 mm (B) L200 CM,r0.4 mm (C)300 CM, r 0.6 mm(D) L400 CM, r0.8 mm

Answer 1

Answer:

largest extension is in option A

Explanation:

Formula for calculating the change in length when a wire is stretched;

∆L = (f x L)/(Y x A)

In our case, f and Y are constant, so ∆L is maximum when   ( L)/A  is maximum or we can say that ( L)/d^2  is maximum.

Now applying this to all the four options;

Option A :  ∆L = ( 2000)/〖0.4〗^2  = 12500

Option B :  ∆L = ( 2000)/〖0.8〗^2  = 3125

Option C :  ∆L = ( 3000)/〖1.2〗^2  = 2083.3

Option D :  ∆L = ( 4000)/〖1.6〗^2  = 1562.5

Now comparing all the options, largest extension is in option A

Answer 2

Answer:

length=50cm and diameter=0.5mm

Explanation:

Y=FL/πr²l

l=FL/πr²Y

l proportional to L/r²

so , lesser the radius more the extension in the wire

hope it helps