Question

A glass full of water has a bottom of area 20 cm², top of area 20 cm², 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 = 1.0 x 10⁵ N/m². Density of water = 1000 kg/m³ and g = 10 m/s². Take all numbers to be exact.

Answer 1

We know that the Pressure  at the bottom will be given by the relation,

The pressure of water at the bottom = ρgh + Atmospheric Pressure

= 1000 × 10 × 0.20 +  1.013  × 10⁵

= 1.02 × 10⁵ Pa.

Hence the force by the water on the bottom  

= 1.02 x 10⁵ × 20 × 10⁻⁴

= 204 N

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(b) Now, The Resultant force from the sides to the water will be given by,        

  =  mg + P × A

=0.5 × 10 + 20 × 10⁻⁴ ×  1.0 x 10⁵ N

= 5 + 200 N

= 205 N

Now, Force by the bottom of the glass on the water is equal but opposite to that of the force by the water on the bottom = 204 N

Hence the force by the sides of the glass on the water = F - P

= 205 - 204

= 1 N

Hope it helps .

Answer 2

(a) 204 N

(b) 1 N

hope this could help