5. A wire of resistance “R” is stretched till its radius is half of the original value. The resistance of stretched wire is:

The resistance (R) of a wire is given by the formula:

R = ρL/A

where: ρ is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire.

When the wire is stretched, its volume remains constant. The volume of the wire can be given by the formula:

V = AL = πr²L

where: r is the radius of the wire.

When the radius of the wire is halved, the new radius is r/2. Substituting this into the volume formula gives:

V = π(r/2)²L'

where: L' is the new length of the wire.

Solving for L' gives:

L' = 4L

Substituting this into the resistance formula gives:

R' = ρL'/A' = ρ(4L)/(π(r/2)²) = 16ρL/πr² = 16R

So, the resistance of the stretched wire is 16 times the original resistance.