COOLING \[=\FRAC{d\theta }{dt}=\] slope of the curve. At \[P,\frac{d\theta }{dt}=\TAN {{\phi }_{2}}=k({{\theta }_{2}}-{{\theta }_{0}})\], where k=constant. At \[Q\frac{d\theta }{dt}=\tan {{\phi }_{1}}=k({{\theta }_{1}}-{{\theta }_{0}})\] \[\Rightarrow \frac{\tan {{\phi }_{2}}}{\tan {{\phi }_{1}}}=\frac{{{\theta }_{2}}-{{\theta }_{0}}}{{{\theta }_{1}}-{{\theta }_{0}}}\]

"> COOLING \[=\FRAC{d\theta }{dt}=\] slope of the curve. At \[P,\frac{d\theta }{dt}=\TAN {{\phi }_{2}}=k({{\theta }_{2}}-{{\theta }_{0}})\], where k=constant. At \[Q\frac{d\theta }{dt}=\tan {{\phi }_{1}}=k({{\theta }_{1}}-{{\theta }_{0}})\] \[\Rightarrow \frac{\tan {{\phi }_{2}}}{\tan {{\phi }_{1}}}=\frac{{{\theta }_{2}}-{{\theta }_{0}}}{{{\theta }_{1}}-{{\theta }_{0}}}\]

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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 \[P(\theta ={{\theta }_{1}})\]and\[Q(\theta ={{\theta }_{2}})\]. These tangents meet the time axis at angles of \[{{\phi }_{2\,}}\] and \[{{\phi }_{1}}\], as shown

NEET Physics in NEET 1 year ago

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[b] For \[\theta -t\] plot, rate of COOLING \[=\FRAC{d\theta }{dt}=\] slope of the curve. At \[P,\frac{d\theta }{dt}=\TAN {{\phi }_{2}}=k({{\theta }_{2}}-{{\theta }_{0}})\], where k=constant. At \[Q\frac{d\theta }{dt}=\tan {{\phi }_{1}}=k({{\theta }_{1}}-{{\theta }_{0}})\] \[\Rightarrow \frac{\tan {{\phi }_{2}}}{\tan {{\phi }_{1}}}=\frac{{{\theta }_{2}}-{{\theta }_{0}}}{{{\theta }_{1}}-{{\theta }_{0}}}\]

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Posted on 04 Sep 2024, this text provides information on NEET related to Physics in NEET. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.

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