The Young’s modulus of brass and steel are 10×1010N m−2 and 2× 1011 N m−2 respectively. A brass wire and a steel wire of the same length are extended by 1 mm under the same force. The radii of the brass and steel wires are RB and Rs respectively. Then
Y=Fπ R2×1△ l
F, l and △ l are constants
Therefore R2 ∝1Y
R2SR2B=YBYS=10112×1011= 12
or RSRB=1√2or Rs=RB√2