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# A body cools in a surrounding which is at a constant temperature of ${\theta }_{0}$. Assume that it obeys Newton's law of cooling. Its temperature $\theta$ is plotted against time t. Tangents are drawn to the curve at the points $P\left(\theta ={\theta }_{2}\right)$ and $Q\left(\theta ={\theta }_{1}\right)$. These tangents meet the time axis at angles of ${\varphi }_{2}$ and ${\varphi }_{1}$, as

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a
tan⁡ϕ2tan⁡ϕ1=θ1−θ0θ2−θ0
b
tan⁡ϕ2tan⁡ϕ1=θ2−θ0θ1−θ0
c
tan⁡ϕ1tan⁡ϕ2=θ1θ2
d
tan⁡ϕ1tan⁡ϕ2=θ2θ1
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detailed solution

Correct option is B

For θ−t plot, rate of cooling =dθdt= slope of the curve.  At  P,dθdt=tan⁡ϕ2=k(θ2−θ0), where k= constant.  At  Q, dθdt=tan⁡ϕ1=kθ1−θ0⇒tan⁡ϕ2tan⁡ϕ1=θ2−θ0θ1−θ0

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