Final answer:
The work necessary for stretching another wire of the same material but with double the radius and half the length by 1 mm is B. 4 J.
Step-by-step explanation:
To find the work necessary for stretching another wire of the same material but with double the radius and half the length by 1 mm, we can use the formula for work:
Work = Force × Displacement
Since the wire is being stretched by 1 mm, the displacement is 0.001 m. The force can be calculated using Hooke's law:
Force = spring constant × displacement
Now, let's consider the differences in radius and length between the two wires:
- The second wire has double the radius: If the radius of the first wire is r, then the radius of the second wire is 2r.
- The second wire has half the length: If the length of the first wire is L, then the length of the second wire is L/2.
Therefore, the spring constant of the second wire is:
spring constant = (spring constant of first wire) × (radius of second wire / radius of first wire) × (length of second wire / length of first wire)
Now we can plug in the values:
spring constant = (2 J / 0.001 m) × (2r / r) × (L / (L/2)) = 4 J
Finally, we can calculate the work for stretching the second wire:
Work = Force × Displacement = (4 J) × (0.001 m) = 0.004 J
Therefore, the work necessary for stretching another wire of the same material but with double the radius and half the length by 1 mm is 0.004 J, which is equal to 4 J.