A wire of resistance 'R' is stretched till its radius is half of the original value. The 2R resistance of stretched wire is:

Explanation

The resistance (R) of a wire is given by formula: R = ρ L/Awhere ( ρ ) is the resistivity of the material, ( L ) is the length of the wire, and ( A ) is the cross-sectional area.When the wire is stretched and its radius is halved, its cross-sectional area ( A ) becomes one-fourth, since ( A ) is proportional to the square of the radius (( r2 )). However, the volume (and thus the mass) of the wire remains constant, so the length ( L ) of the wire must increase to compensate for the reduced cross-sectional area.The new resistance ( R' ) of the wire can be found by substituting the new length ( L' ) and new area ( A' ) into the resistance formula: R' = ρ L'/A'Given that ( L' ) is the new length and ( A' ) is the new area, which is one-fourth of the original area, we can express ( L' ) in terms of the original length ( L ) due to the conservation of volume: L′= 4LSubstituting ( L' ) and ( A' ) into the formula for ( R' ), we get: R′ = 4L/(1/4)A =16ρL/A =16RTherefore, the new resistance of the wire when its radius is halved is 16R.