The resistance of a conductive wire is given by:

where

is the material resistivity

is the wire length

is the cross-sectional area of the wire
The length of the wire is quadrupled, so if we call L the original length and L' the new length, we can write

Similarly, the radius of the wire is doubled (r'=2r), so the new area is

And if we substitute into the equation, we find that the new resistance of the wire is

Therefore, R=R': this means that the resistance of the wire did not change.
Answer:

Explanation:
According to Coulomb's law, the magnitude of the electric force between two equals charges (q) is given by:

Here k is the coulomb constant and d is the distance between the charges. For two electrons we have:

Answer: 50J
Explanation:
Mechanical energy follows the same principles of kinetic energy and potential energy, it is conserved. So Ei = Ef.
Mechanical energy is the sum of ALL energy's. There is no friction, so its just kinetic plus potential.
37.5 + 12.5 = 50J
Since the particle has not touched the ground, it has not transferred any energy to the ground yet, therefore the mechanical energy must still be 50J; mostly in kinetic energy with a very small amount of potential because of the low height relative to the ground.
Answer:
The length of the rod should be

Explanation:
Period of simple pendulum is given by

We have

The length of the rod should be
