question_answer

Two rods of the same length, same cross sectional area and same material transfer a given amount of heat, in 12 seconds when they are joined end to end. But when they are joined lengthwise, they will transfer the same amount of heat, in the same conditions, in

A) 24 s                             

B) \[3\,s\]                

C)        \[1.5\,s\]          

D)      \[48\,s\]                       

Correct Answer: B

Solution :

When the rods are joined in series (end to end), then equivalent Conductivity is K/2 \[{{Q}_{1}}=\frac{(k/2)A.\Delta \theta {{t}_{1}}}{\ell }\] If the rods are joined in parallel (lengthwise) the equivalent conductivity is 2 k Hence, \[{{Q}_{2}}=\frac{(2.k)A.\Delta \theta {{t}_{2}}}{\ell }\] Now \[{{Q}_{1}}={{Q}_{2}}(Given)\] \[\frac{(k/2)A.\Delta \theta {{t}_{1}}}{\ell }=\frac{(2.k)A.\Delta \theta {{t}_{2}}}{\ell }\] \[\Rightarrow \]\[{{t}_{2}}=\frac{{{t}_{1}}}{4}=\frac{12}{4}=3\,s.\] Hence, the correction option is (b).