Q.

A body cools in a surrounding which is at a constant temperature of θ0. Assume that it obeys Newton's law of cooling. Its temperature θ is plotted against time t. Tangents are drawn to the curve at the points Pθ=θ2 and Qθ=θ1. These tangents meet the time axis at angles of ϕ2 and ϕ1, as

Moderate

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tan⁡ϕ2tan⁡ϕ1=θ1−θ0θ2−θ0

tan⁡ϕ2tan⁡ϕ1=θ2−θ0θ1−θ0

tan⁡ϕ1tan⁡ϕ2=θ1θ2

tan⁡ϕ1tan⁡ϕ2=θ2θ1

answer is 2.

(Detailed Solution Below)

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Detailed Solution

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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