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 the same surface temperature- the value of x is -displaystyle frac-1-4-displaystyle frac-1-3-34

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Toppr Admin · Accepted Answer

From Newton-apos-s law of cooling-dTdt-x2212-4-x3C3-eAT30ms-T-x2212-T0-x2212-4-x3C3-e-4-x3C0-r2-T30-x3C1-4-3-x3C0-r3-s-T-x2212-T0-Thus- dTdt-x221D-1r

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 :141334

From Newton's law of cooling,dTdt=−4σeAT30ms(T−T0)=−4σe(4πr2)T30(ρ4/3πr3)s(T−T0)Thus, dTdt∝1r

From Newton's law of cooling,
$\frac{d T}{d t} = - \frac{4 σ e A T_{0}^{3}}{m s} (T - T_{0}) = - \frac{4 σ e (4 π r^{2}) T_{0}^{3}}{(ρ 4 / 3 π r^{3}) s} (T - T_{0})$
Thus, $\frac{d T}{d t} \propto \frac{1}{r}$