Water from a leaking tap begins to fall into
an empty tank 0.5 m wide by 2 m long by
4 m high. If the drops fall at a rate of 2 drops
per second, and if each drop weighs 0.05 g,
after how many seconds will the pressure at
the bottom of the tank be 200 Pa?
[Density of water = 1000 kgm and
g= 10 ms ?]

It will take 20,000 seconds to get a pressure of 200Pa at the bottom of the tank.

Explanation:

The pressure at the bottom of the tank will be

where is the mass of the water, and is the base area of the tank.

The base area of the tank is

,

and if we want the pressure at the bottom to be 200pa, then it must be that

,

solving for we get:

which is the required mass of the water in the tank.

Now, the tank fills at a rate of 2 drops per second or

since each drop weights 0.05g.

Therefore, the time it takes to collect 20kg of water will be

which is 55.56 hours or 2 days and 7.56 hours.

Thus, it will take 20,000 seconds to get a pressure of 200Pa at the bottom of the tank.

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