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 angle of `phi_(2)` and`phi_(1)` as shown
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Options

A. `(tan phi_(2))/(tan phi_(1))=(theta_(1)-theta_(0))/(theta_(2)-theta_(0))`
B. `(tan phi_(2))/(tan phi_(1))=(theta_(1)-theta_(0))/(theta_(2)-theta_(0))`
C. `(tan phi_(2))/(tan phi_(1))=(theta_(1)-theta_(0))/(theta_(2)-theta_(0))`
D. `(tan phi_(2))/(tan phi_(1))=(theta_(1)-theta_(0))/(theta_(2)-theta_(0))`

Answer

B

Explanation

For `theta -t` plot, rate of cooling ` =(dQ)/(dt)` slope of the curve
`ATP, (d theta)/(dt) = |tan (180 -phi_(2)) =tan phi_(2) =k(theta_(2) -theta_(0))`
where k =constant
`At Q, (d theta)/(dt) =|tan (180 - singma_(1)) = tan phi_(1) =k(theta_(1) -theta_(0))`
`:.(tanphi_(2))/(tanphi_(1))=(theta_(2)-theta_(0))/(theta_(1)-theta_(0))` .