Differential Equations 3 Question 8
8. A spherical rain drop evaporates at a rate proportional to its surface area at any instant $t$. The differential equation giving the rate of change of the rains of the rain drop is
(1997C, 2M)
Analytical & Descriptive Questions
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Answer:
Correct Answer: 8. $\frac{d r}{d t}=-\lambda$
Solution:
- Since, rate of change of volume $\propto$ surface area
$$ \begin{array}{lll} \Rightarrow & \frac{d V}{d t} & \propto SA \\ \Rightarrow & & 4 \pi r^{2} \cdot \frac{d r}{d t}=-\lambda 4 \pi r^{2} \end{array} $$
$\frac{d r}{d t}=-\lambda$ is required differential equation.
