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One end of a two-dimensional water tank has the shape of a quadrant of a circle of radius 2 m. When the tank is full, the vertical component of the force per unit length on the curved surface will be
- a)9.81π kN
- b)19.62 π kN
- c)29.43π kN
- d)39.24π kN
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
One end of a two-dimensional water tank has the shape of a quadrant of...
B)Zero
c)6.28
d)3.14
The correct answer is d) 3.14.
Explanation:
The vertical component of the force per unit length on the curved surface is given by:
F = ρgH
where ρ is the density of water, g is the acceleration due to gravity, and H is the height of the water column above the curved surface.
In this case, the curved surface is the quadrant of a circle of radius 2 m. The height of the water column above the curved surface will be equal to the height of the quadrant, which is also 2 m.
Therefore, H = 2 m.
Substituting this value into the equation for F, we get:
F = ρg(2 m) = 2ρg
Since ρ and g are constants, the vertical component of the force per unit length on the curved surface is also constant and equal to 2ρg.
Now, we need to determine the value of 2ρg.
The density of water is approximately 1000 kg/m³, and the acceleration due to gravity is approximately 9.81 m/s².
Substituting these values into the equation for F, we get:
F = 2ρg = 2(1000 kg/m³)(9.81 m/s²) = 19620 N/m
This is the total force per unit length on the curved surface. However, we are only interested in the vertical component of this force.
Since the curved surface is a quadrant of a circle, we can use the formula for the area of a quadrant to find the length of the curved surface:
A = (1/4)πr²
where r is the radius of the circle.
Substituting r = 2 m, we get:
A = (1/4)π(2 m)² = π m²
Therefore, the vertical component of the force per unit length on the curved surface is:
Fv = F/A = (19620 N/m)/(π m²) ≈ 3.14 N/m
So the correct option is d) 3.14.
c)6.28
d)3.14
The correct answer is d) 3.14.
Explanation:
The vertical component of the force per unit length on the curved surface is given by:
F = ρgH
where ρ is the density of water, g is the acceleration due to gravity, and H is the height of the water column above the curved surface.
In this case, the curved surface is the quadrant of a circle of radius 2 m. The height of the water column above the curved surface will be equal to the height of the quadrant, which is also 2 m.
Therefore, H = 2 m.
Substituting this value into the equation for F, we get:
F = ρg(2 m) = 2ρg
Since ρ and g are constants, the vertical component of the force per unit length on the curved surface is also constant and equal to 2ρg.
Now, we need to determine the value of 2ρg.
The density of water is approximately 1000 kg/m³, and the acceleration due to gravity is approximately 9.81 m/s².
Substituting these values into the equation for F, we get:
F = 2ρg = 2(1000 kg/m³)(9.81 m/s²) = 19620 N/m
This is the total force per unit length on the curved surface. However, we are only interested in the vertical component of this force.
Since the curved surface is a quadrant of a circle, we can use the formula for the area of a quadrant to find the length of the curved surface:
A = (1/4)πr²
where r is the radius of the circle.
Substituting r = 2 m, we get:
A = (1/4)π(2 m)² = π m²
Therefore, the vertical component of the force per unit length on the curved surface is:
Fv = F/A = (19620 N/m)/(π m²) ≈ 3.14 N/m
So the correct option is d) 3.14.
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Community Answer
One end of a two-dimensional water tank has the shape of a quadrant of...
Vertical component of force=(1000×9.81×π×2^2)/(1000×4)=9.81π kN
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One end of a two-dimensional water tank has the shape of a quadrant of a circle of radius 2 m. When the tank is full, the vertical component of the force per unit length on the curved surface will bea)9.81π kNb)19.62π kNc)29.43π kNd)39.24π kNCorrect answer is option 'A'. Can you explain this answer?
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