An oil tank has a base of area 2.5 m2 and is filled with oil to a depth of 1.2 m. Thedensity of the oil is 800 kg/ m3. What is the force exerted on the base of the tank due to theoil?A 960N B 2400N C 9400N D 24 000N
Question
An oil tank has a base of area 2.5 m2 and is filled with oil to a depth of 1.2 m. Thedensity of the oil is 800 kg/ m3. What is the force exerted on the base of the tank due to theoil?A 960N B 2400N C 9400N D 24 000N
Solution
To solve this problem, we need to use the formula for pressure in a fluid at a certain depth, which is P = ρgh, where:
- P is the pressure,
- ρ is the fluid density,
- g is the acceleration due to gravity, and
- h is the height of the fluid above the point in question.
Step 1: Substitute the given values into the formula
The density ρ is given as 800 kg/m³, the acceleration due to gravity g is approximately 9.8 m/s², and the height h is 1.2 m. Substituting these values into the formula gives:
P = 800 kg/m³ * 9.8 m/s² * 1.2 m = 9408 Pa (Pascal)
Step 2: Convert the pressure into force
Pressure is defined as force per unit area. Therefore, to get the force, we multiply the pressure by the area. The area of the base of the tank is given as 2.5 m². Therefore, the force F is:
F = P * A = 9408 Pa * 2.5 m² = 23520 N
So, the force exerted on the base of the tank due to the oil is approximately 23520 N. This is not exactly one of the options given, but it is closest to option D, 24 000N.
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