Question

A rod of 2 cm diameter and 30 cm length is converted into a wire of 3 m length of uniform thickness. The diameter of the wire is:

Options

• `2/10` cm

• `2/sqrt10` cm

• `1/sqrt10` cm

• `1/10` cm

Answer 1

`1/sqrt10` cm

Explanation:

Radius of rod = `2/2` = 1 cm

Height = 30 cm

Converted to wire of length = 3m, = 300 cm

r = ?

V₁ = V₂

πr²h = πR²H

π(1)² × 30 = πR² × 300 

`"R"^2 = 1/10 = sqrt(1/10)  "cm" = 1/sqrt10 "cm"`