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

Show Answer

Answer:

Correct Answer: 8. $\frac{d r}{d t}=-\lambda$

Solution:

  1. 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.



NCERT Chapter Video Solution

Dual Pane