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A spherical raindrop loses volume by evaporation at a rate proportional to its surface area. If K > 0 is the proportionality constant, the differential equation governing the rate of change of its radius r is:
- dr/dt + K = 0
- dr/dt - K = 0
- dr/dt = K*r
- none
Correct answer: dr/dt + K = 0
Solution
Since dV/dt = -K*(4*pi*r²) and dV/dt = 4*pi*r²*(dr/dt), it follows that dr/dt = -K, i.e. dr/dt + K = 0.
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