A body cools in a surrounding which is at a constant temperature of $\theta _0$ . Assuming 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 $A(\theta = \theta _1)$ and $B(\theta = \theta _2)$ . These tangents meet the time-axis at angles $\alpha _1$ and $\alpha _2$ as shown in the graph then
A body cools in a surrounding which is at a constant temperature of $\theta _0$ . Assuming 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 $A(\theta = \theta _1)$ and $B(\theta = \theta _2)$ . These tangents meet the time-axis at angles $\alpha _1$ and $\alpha _2$ as shown in the graph then
- A
$\frac{{\tan \,{\alpha _1}}}{{\tan \,{\alpha _2}}} = \frac{{{\theta _2}}}{{{\theta _1}}}$
- B
$\frac{{\tan \,{\alpha _1}}}{{\tan \,{\alpha _2}}} = \frac{{{\theta _1}}}{{{\theta _2}}}$
- C
$\frac{{\tan \,{\alpha _1}}}{{\tan \,{\alpha _2}}} = \frac{{{\theta _1} - {\theta _0}}}{{{\theta _2} - {\theta _0}}}$
- D
$\frac{{\tan \,{\alpha _1}}}{{\tan \,{\alpha _2}}} = \frac{{{\theta _2} - {\theta _0}}}{{{\theta _1} - {\theta _0}}}$
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