a copper rod of diameter 1cm and length 10cm is drawn into a thin wire of length 40m of uniform thickness find the diameter of the wire.
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Given ;
•In a copper rod ->
Radius = 1/2 = 0.5 cm
length = h = 10 cm
• In the wire
length = h' = 40m = 4000 cm
Radius = r' = ?
Volume of rod = volume of wire
πr^2 h = πr'^2h'
(0.5×0.5)×10 = (r'^2)×4000
r'^2 = 25/40000
= (5×5)/(200×200)
r' = 5/200
r' = 1/40
r' = 0.025 cm
Diameter of the wire = 2r'
= 0.05 cm
______________________
•In a copper rod ->
Radius = 1/2 = 0.5 cm
length = h = 10 cm
• In the wire
length = h' = 40m = 4000 cm
Radius = r' = ?
Volume of rod = volume of wire
πr^2 h = πr'^2h'
(0.5×0.5)×10 = (r'^2)×4000
r'^2 = 25/40000
= (5×5)/(200×200)
r' = 5/200
r' = 1/40
r' = 0.025 cm
Diameter of the wire = 2r'
= 0.05 cm
______________________
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