A) both the cube and the sphere cool down at the same rate
B) the cube cools down faster than the sphere
C) the sphere cools down faster than the cube
D) whichever is having more mass will cool down faster
Correct Answer: B
Solution :
Rate of cooling of a body R\[=\frac{\Delta \theta }{t}=\frac{A\varepsilon \sigma ({{T}^{4}}-{{T}_{0}}^{4})}{mc}\] \[\Rightarrow R\propto \frac{A}{m}\propto \frac{Area}{Volume}[m=\rho \times V]\] \[\Rightarrow \] For the same surface area. \[R\propto \frac{1}{Volume}\] Volume of cube < Volume of sphere \[\Rightarrow {{R}_{cube}}>{{R}_{sphere}}\] Sphere i.e., cube, cools down with faster rate.
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