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.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 0.1 cm
Stretching changes the shape of the metal but not its volume, so the volume of the wire equals the volume of the rod. Both are cylinders, of volume \(\pi r^2h\).
Volume of the rod \(=\pi\times2^2\times10=40\pi\,\mathrm{cm^3}\)
Length of the wire \(=40\,\mathrm{m}=4000\,\mathrm{cm}\) (both lengths must be in the same unit)
Volume of the wire: \(\pi r^2\times4000=40\pi\), so \(r^2=0.01\)
Radius of the wire \(r=0.1\,\mathrm{cm}\)