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  • Provide solution for RD Sharma maths class 12 chapter Differential Equation exercise 21.2 question 11

Provide solution for RD Sharma maths class 12 chapter Differential Equation exercise 21.2 question 11

Answers (1)

Answer:

 \frac{\mathrm{d} r}{\mathrm{d} t}=-k

Hint:

 Let the surface be A

Rate of evaporation,

\frac{\mathrm{d} v}{\mathrm{d} t}

Using formula,

v=\frac{4}{3}\pi r^{3},\quad A=4\pi r^{2}

Given:

 Rain drop evaporates at a rate proportional to its surface area

Solution:

\begin{aligned} &\frac{\mathrm{d} v}{\mathrm{d} t}\propto A \\ &\frac{\mathrm{d} v}{\mathrm{d} t}=-kA \\ &\frac{\mathrm{d} }{\mathrm{d} t}\left ( \frac{4}{3}\pi r^{3} \right )=-k(4\pi r^{2}) \\ &\frac{4}{3}\pi (3r^{2})\frac{\mathrm{d} r}{\mathrm{d} t}=-4\pi r^{2} \\ &\frac{\mathrm{d} r}{\mathrm{d} t}=-k \end{aligned}

Posted by

Gurleen Kaur

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