A wire \(P\) of length \(L\) made of a material of density \(D\) and Young's modulus \(Y\) elongates by \(2.0\) mm under its own weight. If another wire \(Q\) made of a material of density
\[
\frac{2D}{3}
\]
and Young's modulus
\[
\frac{3Y}{4}
\]
elongates by \(1.0\) mm under its own weight, then the length of the wire \(Q\) is
Show Hint
For a uniform wire suspended vertically,
\[
\boxed{
\Delta l=\frac{\rho gL^2}{2Y}.
}
\]
Notice that the elongation is proportional to
\[
\boxed{\frac{\rho L^2}{Y}.}
\]