Answer:
Option B
Explanation:
Body cools from 70° C to 40°C in 5 minute, hence , $T_{1}=70^{0}C, T_{2}=40^{0}C$ and t=5 minute
Temperature of surrounding , $T_{0}=20^{0}C$
By Newton's law of cooling,
$\frac{T_{1}-T_{2}}{t}=k\left[\frac{T_{1}+T_{2}}{2}-T_{0}\right]$
or $\frac{70-40}{5}=k\left[\frac{70+40}{2}-20\right]\Rightarrow k= \frac{6}{35}$ ...........(i)
Again, let body cools from $60^{0}$C to $30^{0} C$ in time t minutes.
i.e, $T_{1}'=60^{0} C$ and $T_{2}'=30^{0}C$,
$\therefore$ By Newton's law of cooling
$\frac{T_{1}'-T_{2}'}{t}=k\left[\frac{T_{1}'+T_{2}'}{2}-T_{0}\right]$
$\frac{60-30}{t}=\frac{6}{35}\left[\frac{60+30}{2}-20\right]$ [ $\because $ From eq.(i)]
$\frac{30}{t}=\frac{6}{35}[25] \Rightarrow $ t=7 minutes
Hence, option (b) is correct
