A solid sphere and a hollow sphere of the same material and size are heated to the same temperature and allowed to cool in the same surroundings. If the temperature difference between each sphere and its surroundings is $T$, then
A solid sphere and a hollow sphere of the same material and size are heated to the same temperature and allowed to cool in the same surroundings. If the temperature difference between each sphere and its surroundings is $T$, then
- A
The hollow sphere will cool at a faster rate for all values of $T$
- B
The solid sphere will cool at a faster rate for all values of $T$
- C
Both spheres will cool at the same rate for all values of $T$
- D
Both spheres will cool at the same rate only for small values of $T$
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Two bottles $A$ and $B$ have radii $R_{A}$ and $R_{B}$ and heights $h_{A}$ and $h_{B}$ respectively, with $R_{B}=2 R_{A}$ and $h_{B}=2 h_{A}$. These are filled with hot water at $60^{\circ} C$. Consider that heat loss for the bottles takes place only from side surfaces. If the time, the water takes to cool down to $50^{\circ} C$ is $t_{A}$ and $t_{B}$ for bottles $A$ and $B$, respectively. Then, $t_{A}$ and $t_{B}$ are best related as
Two bottles $A$ and $B$ have radii $R_{A}$ and $R_{B}$ and heights $h_{A}$ and $h_{B}$ respectively, with $R_{B}=2 R_{A}$ and $h_{B}=2 h_{A}$. These are filled with hot water at $60^{\circ} C$. Consider that heat loss for the bottles takes place only from side surfaces. If the time, the water takes to cool down to $50^{\circ} C$ is $t_{A}$ and $t_{B}$ for bottles $A$ and $B$, respectively. Then, $t_{A}$ and $t_{B}$ are best related as
- [KVPY 2017]
A metallic sphere cools from $50^{\circ} C$ to $40^{\circ} C$ in $300 \,s.$ If atmospheric temperature around is $20^{\circ} C ,$ then the sphere's temperature after the next $5$ minutes will be close to$.....C$
A metallic sphere cools from $50^{\circ} C$ to $40^{\circ} C$ in $300 \,s.$ If atmospheric temperature around is $20^{\circ} C ,$ then the sphere's temperature after the next $5$ minutes will be close to$.....C$
- [JEE MAIN 2020]