If a metallic rod of 10 cm length and 2 cm radius is stretched into a wire of 40 m length having uniform thickness, then find the radius of the stretched wire.

0.1 cm

The correct answer is Option (3) → 0.1 cm

When a rod is stretched into a wire, volume remains constant.

Given:

• Length of rod $L_1 = 10$ cm
• Radius of rod $r_1 = 2$ cm
• Length of wire $L_2 = 40$ m = 4000 cm
• Radius of wire $r_2 = ?$

Volume before = Volume after

$\pi r_1^2 L_1 = \pi r_2^2 L_2$

Cancel $\pi$:

$(2)^2 \times 10 = r_2^2 \times 4000$

$40 = 4000 r_2^2$

$r_2^2 = \frac{40}{4000} = \frac{1}{100}$

$r_2 = \sqrt{\frac{1}{100}} = \frac{1}{10} = 0.1 \text{ cm}$