The diameter that the the new wire will have is A. r/R = ✓2.
How is the stretching illustrated?
When a spring is stretched or compressed by an amount x from its equilibrium length, it exerts a force F = -kx in the direction of its equilibrium position. The force exerted by a spring is a restoring force, acting to return the spring to its equilibrium length.
Pulling forces cause stretching. We must pull on a spring to stretch it. This can be accomplished by attaching some small weights to the end of the spring, causing it to change length.
As there is no stretching, the volume of the wire will be the same after the length doubling.
r = diameter when the length was L
R = diameter when the length is 2L.
Conserving volume
πr²L = πR² (2L)
r/R = ✓2.
The correct option is Option A.
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