Question:
A copper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18 m of uniform thickness find the thickness of the wire
Answer:
Given diameter of the copper rod = 1 cm
So, radius(r) of the copper rod = 1/2 cm
Let R is the radius of the cross section(circular) of the wire.
Now, according to the question,
πR2 *(18*100) = π(1/2)2 *8
=> R2 *(18*100) = (1/2)2 *8
=> R2 *(18*100) = 8/4
=> R2 *(18*100) = 2
=> R2 = 2/(18*100)
=> R2 = 1/(9*100)
=> R = √{1/(9*100)}
=> R = 1/(3*10)
=> R = 1/30
Now, thickness of the wire = 2r = 2 * 1/30 = 2/30 = 1/15 = 0.067 cm
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