Two rectangular blocks $A$ and $B$ of different metals have same length and same area of cross-section. They are kept in such a way that their cross-sectional area touch each other. The temperature at one end of $A$ is $100°C$ and that of $B$ at the other end is $0°C$ . If the ratio of their thermal conductivity is $1 : 3$ , then under steady state, the temperature of the junction in contact will be ........ $^oC$

  • A

    $25$

  • B

    $50$

  • C

    $75$

  • D

    $100$

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  • [JEE MAIN 2022]

$Assertion :$ Woolen clothes keep the body warm in winter
$Reason :$ Air is a bad conductor of heat.

  • [AIIMS 2002]

Two rods (one semi-circular and other straight) of same material and of same cross-sectional area are joined as shown in the figure. The points $A$ and $B$ are maintained at different temperature. The ratio of the heat transferred through a cross-section of a semi-circular rod to the heat transferred through a cross section of the straight rod in a given time is