a copper wire ,3mm in diameter is wound about a cylinder whose length is 12 cm ,and diameter 10 cm,so as to cover the curved surface area of a cylinder .find the length and the mass of wire ,assuming the density of copper to be 8.88 gm per cm
find the answer
Radius of cylinder = 10/2 = 5 cm
CSA of cylinder = 2πRL = 2x3.14x5x12 = 376.8 cm2
Area covered in one turn of the given copper wire, 2πRD , where D is the diameter of the copper wire.
Hence number of turns of copper wire = CSA of cylinder/Area covered in one turn
= 2πRL/2πRD = L/D = 120 mm/3mm = 40 turns.
Total length of the wire = 2πRx number of turns = 2x3.14x5x40 = 1256 cm
Total mass of the wire = DensityxVolume
= Densityx π r2 x Length of wire ........r - radius of copper wire, 3/2 = 1.5 mm = 0.15 cm
= 8.88 x 3.14 x 0.15 x 0.15 x 1256 = 787.98 gm