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A body cools in a surrounding which is a...

A body cools in a surrounding which is at constant temperature of `theta_(0)`. Assume that it obeys Newton's law of colling. Its temperature `theta` is plotted against time `t`. Tangents are drawn to the curve at the points `P(theta=theta_(t))` and `Q(theta=theta_(2))`. These tangents meet the time axis at angles of `phi_(2)` and `phi_(1)`, as shown

A

`(tan phi_2)/(tan phi_1)=(theta_1 - theta_0)/(theta_2-theta_0)`

B

`(tan phi_2)/(tan phi_1)=(theta_2 - theta_0)/(theta_1-theta_0)`

C

`(tanphi_1)/(tan phi_2)=(theta_1)/(theta_2)`

D

`(tan phi_1)/(tan phi_2)=(theta_2)/(theta_1)`

Text Solution

Verified by Experts

The correct Answer is:
B
`(d theta)/(dt)` = slope of the curve
At `P, (d theta)/(dt)=tan phi_2=k(T_2 - T_0)`
At Q , `(d theta)/(dt)= tan phi_1=k(T_1-T_0)`
`therefore (tan phi_2)/(tan phi_1)=((T_2-T_0)/(T_1-T_0))`
`T_2=theta_2` and `T_1=theta_1,T_0=theta_0`
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