A body obeying Newton's law of cooling cools in a surrounding which is at a constant temperature Its temperature `theta` is plotted against time There are two points on the curve with temperatures `theta_(2)` and `theta_(1)(theta_(2) gttheta_(1))` such that tangents on these points make angles of `2phi` and half of its with time axis respectively Find the temperature of the surrounding .

Options

A. `theta_(1) cos 2phi -theta_(2) (1 +cos 2phi)`
B. `theta_(1) (1+cos 2phi) -theta_(2) cos 2phi`
C. `(theta_(2)-theta_(1)) cos 2phi`
D. `(2theta_(1)+theta_(2)(1+tan^(2)phi))/((1-tan^(2)phi))`

Answer

B

Explanation

`(d theta)/(dt) = |tan (180^(@)-2varphi)|=tan2varphi=K(theta_(2)-theta_(0))`
`(d theta)/(dt)=|tan(180^(@)-varphi|=tna varphi=K(theta_(1)-theta_(0))`
`(tan2varphi)/(tan varphi)=(theta_(2)-theta_(0))/(theta_(1)-theta_(0))`
solving `theta_(0)=theta_(1)(1+cos2varphi)-theta_(2)-con2varphi` .