A glass filled completely with water has a bottom area of 20 cm ^2 , a top area of 20 cm ^2 , a height of 20 cm , and a volume of half a litre. By considering the equilibrium of the water, determine the resultant force exerted by the sides of the glass on the water. The atmospheric pressure is 1.0 10^5 N m ⁻² , the density of water is 1000 kg m ⁻³ , and g = 10 m s ⁻² . Assume all numbers are exact.

Step-by-step solution

For the water to be in equilibrium, the net vertical force acting on it must be zero. The forces acting on the water in the vertical direction are: 1. Weight of the water ( W ) acting downward. 2. Force due to atmospheric pressure on the top surface ( F_ top ) acting downward. 3. Force due to liquid pressure on the bottom surface ( F_ bottom ) acting upward. 4. Resultant force exerted by the sides of the glass ( F_ sides ). Let us assume it acts upward. The weight of the water is: W = V g = 1000 (0.5 10⁻³) 10 = 5 N