a copper wire 6 mm in diameter is evenly wound about cylinder whose length is 24 cm and diameter 20 cm so as the cover the w. s. a of the cylinder .find the length and weight of the wire assuming it's specific gravity to be 8.88 gm/cu.cm.
Answers
Solution:-
It is assumed that one round of copper wire will cover 3 mm or 0.3 cm height of cylinder.
Number of rounds = Height of the cylinder/diameter of the wire
= 12/0.3
= 40 rounds
Now,
The length of the wire required in one round = Circumference of the base of the cylinder
Diameter of the cylinder = 10 cm, so the radius = 5 cm.
circumference = 2πr
= 2*π*5
Length of wire required in one round = 10π
Length of wire required in 40 rounds = 10π*40
= 400*22/7
= 8800/7
Length of the wire = 1257.14 cm
Radius of the wire = 0.3/2 = 0.15 cm
Volume of wire = Area of cross section of wire × length of the wire
= π*r² × 12.57
22/7 × (0.15)² × 1257.14
Volume of the wire = 88.898 cm³
Mass = Density × Volume
= 8.88 × 88.898
Mass = 789.41 gm/s
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