b
(b)Rate of heat flow \(\left( {\frac{Q}{t}} \right) = \frac{{k\pi {r^2}({\theta _1} - {\theta _2})}}{L} \propto \frac{{{r^2}}}{L}\)

\(\therefore\) \(\frac{{{Q_1}}}{{{Q_2}}} = {\left( {\frac{{{r_1}}}{{{r_2}}}} \right)^2}\left( {\frac{{{l_2}}}{{{l_1}}}} \right) = {\left( {\frac{1}{2}} \right)^2} \times \left( {\frac{2}{1}} \right) = \frac{1}{2}\)

==> \({Q_2} = 2{Q_1}\)