question_answer

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 angle of\[{{\phi }_{2}}\] and \[{{\phi }_{1}}\], as shown, then 

A) \[\frac{\tan {{\phi }_{2}}}{\tan {{\phi }_{1}}}=\frac{{{\theta }_{1}}-{{\theta }_{0}}}{{{\theta }_{2}}-{{\theta }_{0}}}\]

B) \[\frac{\tan {{\phi }_{2}}}{\tan {{\phi }_{1}}}=\frac{{{\theta }_{2}}-{{\theta }_{0}}}{{{\theta }_{1}}-{{\theta }_{0}}}\]

C)  \[\frac{\tan {{\phi }_{1}}}{\tan {{\phi }_{2}}}=\frac{{{\theta }_{1}}}{{{\theta }_{2}}}\]

D)  \[\frac{\tan {{\phi }_{1}}}{\tan {{\phi }_{2}}}=\frac{{{\theta }_{2}}}{{{\theta }_{1}}}\]