Spheres P and Q are uniformly constructed from the same material which is a good conductor of heat and the radius of Q is thrice the radius of P. The rate of fall of temperature of P is x times that of Q when both are at the same surface temperature. The value of x is :
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Question

Spheres P and Q are uniformly constructed from the same material which is a good conductor of heat and the radius of Q is thrice the radius of P. The rate of fall of temperature of P is x times that of Q when both are at the same surface temperature. The value of x is :

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G1 Physics · Accepted Answer

Use Stefan-Boltzmann law P=eσA(T⁴−Tₛ⁴), Wien's law λₘT=b, or Newton's law of cooling dθ/dt=−k(θ−θₛ), as applicable. Evaluating the given data/statements gives C: 3. Therefore the correct answer is C.