Physics-
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Question

A body cools in a surrounding which is at a constant temperature of theta subscript 0 end subscript. Assume that of 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 parenthesis theta equals theta subscript 2 end subscript right parenthesis and Q left parenthesis theta equals theta subscript 1 end subscript right parenthesis. These tangents meet the time axis at angles of ϕ subscript 2 end subscript and ϕ subscript 1 end subscript, as shown

  1. fraction numerator tan invisible function application ϕ subscript 2 end subscript over denominator tan invisible function application ϕ subscript 1 end subscript end fraction equals fraction numerator theta subscript 1 end subscript minus theta subscript 0 end subscript over denominator theta subscript 2 end subscript minus theta subscript 0 end subscript end fraction    
  2. fraction numerator tan invisible function application ϕ subscript 2 end subscript over denominator tan invisible function application ϕ subscript 1 end subscript end fraction equals fraction numerator theta subscript 2 end subscript minus theta subscript 0 end subscript over denominator theta subscript 1 end subscript minus theta subscript 0 end subscript end fraction    
  3. fraction numerator tan invisible function application ϕ subscript 1 end subscript over denominator tan invisible function application ϕ subscript 2 end subscript end fraction equals fraction numerator theta subscript 1 end subscript over denominator theta subscript 2 end subscript end fraction    
  4. fraction numerator tan invisible function application ϕ subscript 1 end subscript over denominator tan invisible function application ϕ subscript 2 end subscript end fraction equals fraction numerator theta subscript 2 end subscript over denominator theta subscript 1 end subscript end fraction    

The correct answer is: fraction numerator tan invisible function application ϕ subscript 2 end subscript over denominator tan invisible function application ϕ subscript 1 end subscript end fraction equals fraction numerator theta subscript 2 end subscript minus theta subscript 0 end subscript over denominator theta subscript 1 end subscript minus theta subscript 0 end subscript end fraction


    For theta t plot, rate of cooling equals fraction numerator d theta over denominator d t end fraction equals slope of the curve
    At P comma fraction numerator d theta over denominator d t end fraction equals tan invisible function application ϕ subscript 2 end subscript equals k open parentheses theta subscript 2 end subscript minus theta subscript 0 end subscript close parentheses comma blankwhereblank k equals constant
    At Q comma fraction numerator d theta over denominator d t end fraction equals tan invisible function application ϕ subscript 1 end subscript equals k open parentheses theta subscript 1 end subscript minus theta subscript 0 end subscript close parentheses rightwards double arrow fraction numerator tan invisible function application ϕ subscript 2 end subscript over denominator tan invisible function application ϕ subscript 1 end subscript end fraction equals fraction numerator theta subscript 2 end subscript minus theta subscript 0 end subscript over denominator theta subscript 1 end subscript minus theta subscript 0 end subscript end fraction

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