Leaky tank

Classical Mechanics Level 4

A tank is filled with water and put on a frictionless surface. The tank has a circular hole of radius \(r_1 = 0.5~\mbox{cm}\) and distance \(h_1 = 1~\mbox{m}\) from the top. You want to prevent the tank from moving. In order to do that, you decide to pierce another hole on the opposite side. The distance of your hole from the top of the tank will be \(h_2 = 0.5~\mbox{m}\). What should be the radius in cm of your hole so that the tank doesn't move?

Details and assumptions

  • You pierce the second hole straight after the first one occurred (the height of the water in the tank remains unchanged).
  • The acceleration of gravity is \(-9.8~\mbox{m/s}^2\).
  • The tank is open to the air on the top and all linear dimensions of the tank are much larger than the radii of the holes.

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