A copper wire 3mm in diameter is wound about a cylinder whose length is 1.2 metre and diameter is 10 CM ,so as to cover the curved surface of the cylinder find the length and mass of the wire is roaming the density of copper wire to be 8.8 gram per cm.
Answers
Given :
Diameter of copper wire = 3mm
Length of cylinder = 1.2m
Diameter of cylinder = 10cm
Density of Copper wire = 8.8g/cm
To Find :
Length and mass of the wire.
Solution :
Let us assume n be the number wounds made by the (upper wire around the cylinder
In each wounds the wire covers a height of its diameter (i.e., 3 mm) on the cylinder.
Thus number of wounds made by wire around the cylinder :
n = height of cylinder/diameter of wire.
n = 1.2m/3mm = 120cm/0.3cm = 400 wounds
The length of the wire required in one round = Circumference of the base of the cylinder
circumference of cylinder = 2πr = 2×π×5
Length of wire required in one round = 10π
Length of wire required in 400 rounds = 10π×400
= 4000×22/7
= 88000/7
= 12571.42cm
Thus length of wire used = 12571.42cm
Now
Volume of wire used in each wound :
= πr²l
where
π = 22/7
r = radius of wire
l = length of wire in 1 wound
Calculating Volume of wire used :
= πr²l
= π × (0.15cm)² × ( 2×π×radius of cylinder)
= π × (0.15cm)² × ( 2×π×5cm)
= (22/7)² × 10 × (0.15)²
= 2.22 cm³
Hence the volume of cone used in 400turns
= 400×2.22 = 888cm³
Mass of upper wire used = Density×Volume
= 8.8×888 = 7885.4 g
density is=8.8×888
volume is =7885.4g