# A glass full of water has a bottom of area 20 cm2, top of area 20 cm, height 20 cm and volume half a liter. (a) Find the force exerted by the water on the bottom. (b) Considering the equilibrium of the water, find the resultant force exerted by the sides of the glass on the water. Atmospheric pressure = 10 × 10 N m-2. Density of water = 1000 kg m4 and g = 10 m s-2. Take all numbers to be exact.

(a) The pressure at the bottom of the container (P) is sum of the pressure due to water and the atmospheric pressure.

Here, the density of water,

Now, Force on the bottom of the container , .

Given,

Hence, (ANS)

(b) The net horizontal forces cancel out as the pressure is same at all points lying in the same horizontal plane. The vertical forces (F’) includes the weight of the water and the force due to atmospheric pressure.

We have 0.5 l of water. So the weight will be 0.5 kg.

Thus the Total force is 205 N while the total downward force on the glass is 204 N {from (a)}.

Therefore, the total upward force,

Hence, the total upward force is 1 N.

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