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# Two rods of equal cross - section have their ratio of lengths 1 : 2 . If the ratio of their coefficient of thermal conductivity are in the ratio 3 : 4 , the ratio of time taken for heat transfer for same temperature differance is -

$(a)\;3 :8\qquad(b)\;8 :3 \qquad(c)\;2 : 3\qquad(d)\;3 : 2$

Answer : $2 : 3$
$\large\frac{\bigtriangleup Q}{\bigtriangleup t}=\large\frac{KA}{l}\;\bigtriangleup T$
$t \propto \large\frac{l}{k} \quad \;(for\; \bigtriangleup T and\; A\; same)$
$\large\frac{t_{1}}{t_{2}}=\large\frac{l_{1}}{l_{2}} . \large\frac{k_{2}}{k_{1}}=\large\frac{1}{2} \times \large\frac{4}{3}=\large\frac{2}{3}$