Question

Water from a leaking tap begins to fall into

Answer 1

Answer:

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

$P = \dfrac{Mg}{A}$

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

The base area of the tank is

$A = 0.5m* 2m = 1m^2$,

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

$200Pa = \dfrac{M(10m/s^2)}{1m^2}$,

solving for $M$ we get:

$M = 20kg$

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

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

$2 (0.05g)/s = 0.10g/s = 0.0001kg/s$

since each drop weights 0.05g.

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

$t = 20kg \div \dfrac{0.0001kg}{s}$

$t = 2*10^5s$

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.