$\frac{{{Y_A}}}{{{Y_B}}} = \frac{7}{4}\,\,\,{L_A} = 2m\,\,\,{A_A} = \pi {R^2}$

                     ${L_B} = 1.5\,m\,\,\,\,\,\,\,\,{A_B} = \pi {\left( {2mm} \right)^2}$

$\frac{F}{A} = Y\left( {\frac{\ell }{L}} \right)$

$given\,F\,and\,\ell \,are\,same \Rightarrow \frac{{AY}}{L}\,is\,same$

$\frac{{{A_A}{Y_A}}}{{{L_A}}} = \frac{{{A_B}{Y_B}}}{{{L_B}}}$

$ \Rightarrow \frac{{\left( {\pi {R^2}} \right)\left( {\frac{7}{4}{Y_B}} \right)}}{2} = \frac{{\pi {{\left( {2\,mm} \right)}^2}.{Y_B}}}{{1.5}}$

$R = 1.74\,mm$