Question

A copper rod of diameter 1cm and length 18cm of uniform thickness.find the thickness of the wire​

Answer 1

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

Answer 2

Correct Question:

A Copper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18 cm of uniform thickness. Find the thickness of the wire.

Given:

• Diameter of copper rod = 1cm
• Length of wire with uniform thickness = 18m
• Height of copper rod = 8cm

To find :

• Thickness of the wire.

Solution:

Diameter of copper rod = 1cm

Radius of copper rod = 1/2 cm

The volume of glass rod = πr²h

$: \implies$ π (1/2)² × 8

$: \implies 2π cm^3$

Length of new wire = 18m = 1800cm

If r is the radius (in cm) of cross- section of wire, it's volume = π × r² × 1800 cm³

Therefore, π × r² × 1800 = 2π

$: \implies r^2 = \frac {1}{900}$

$: \implies \bf { r = \frac{1}{30}}$

So, the diameter of cross section, i.e.,the thickness of wire is 1/15 i.e., 0.67mm (approx.)

$\rule{200}4$