Two wires made of the same material are subjected to forces in the ratio of `1:4`. Their lengths are in the ratio `8:1` and diameter in the ration 2:1. Find the ratio of their extensions.
Correct option is (C) 1 : 4
Let radii of both spheres are r and R respectively.
\(\because\) \(\frac rR=\frac12\)
\(\therefore\) Ratio of their surface areas \(=\frac{4\pi r^2}{4\pi R^2}\)
\(=(\frac rR)^2=(\frac12)^2=\frac14\) = 1 : 4