imo class 12 differential equations

A water tank leaks water at a rate proportional to the square root of the volume V of water remaining. The differential equation is:

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A water tank leaks water at a rate proportional to the square root of the volume V of water remaining. The differential equation is:

  • A. dV/dt = k√V
  • B. dV/dt = −k√V
  • C. dV/dt = −k/V
  • D. dV/dt = −k V²

Answer: B) dV/dt = −k√V

Explanation: Leaking means the volume is decreasing over time. Proportional to square root of V means dV/dt = −k√V (where k is a positive constant).

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