b
\(Energy\,of\,catapult = \frac{1}{2} \times {\left( {\frac{{\Delta \ell }}{\ell }} \right)^2} \times Y \times A \times \ell \)

\( = Kinetic\,energy\,of\,the\,ball = \frac{1}{2}\,m{V^2}\)

\(Therefore,\frac{1}{2} \times {\left( {\frac{{20}}{{42}}} \right)^2} \times Y \times \pi  \times {3^2} \times {10^{ - 6}} \times 42 \times {10^{ - 2}}\)

\( = \frac{1}{2} \times 2 \times {10^{ - 2}} \times {\left( {20} \right)^2}\)

\(Y = 3 \times {10^{6\,}}\,N{m^2}\)