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

  1. fraction numerator tan invisible function application phi subscript 2 end subscript over denominator tan invisible function application phi 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 phi subscript 2 end subscript over denominator tan invisible function application phi 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 phi subscript 1 end subscript over denominator tan invisible function application phi 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 phi subscript 1 end subscript over denominator tan invisible function application phi 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 phi subscript 2 end subscript over denominator tan invisible function application phi 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 q-t plot, rate of cooling equals fraction numerator d theta over denominator d t end fraction equalsslope of the curve.
    At P,fraction numerator d theta over denominator d t end fraction equals tan invisible function application phi subscript 2 end subscript equals k left parenthesis theta subscript 2 end subscript minus theta subscript 0 end subscript right parenthesis, where k = constant.
    At Qfraction numerator d theta over denominator d t end fraction equals tan invisible function application phi subscript 1 end subscript equals k left parenthesis theta subscript 1 end subscript minus theta subscript 0 end subscript right parenthesis rightwards double arrow fraction numerator tan invisible function application phi subscript 2 end subscript over denominator tan invisible function application phi 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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