To find the force of gravity acting on the column of water in the tank, we'll go through a detailed step-by-step process.
1. Calculate the Volume of the Water Column:
The volume of the water column can be found using the formula:
[tex]\[
\text{Volume} = \text{Height} \times \text{Area}
\][/tex]
Given:
- Height = 7 meters
- Area = 1.5 square meters
Substituting the values:
[tex]\[
\text{Volume} = 7 \text{ meters} \times 1.5 \text{ square meters} = 10.5 \text{ cubic meters}
\][/tex]
2. Calculate the Mass of the Water:
To find the mass of the water, we need the density of water, which is 1000 kg/m³. The mass can be calculated using the formula:
[tex]\[
\text{Mass} = \text{Volume} \times \text{Density}
\][/tex]
Given:
- Volume = 10.5 cubic meters
- Density of water = 1000 kg/m³
Substituting the values:
[tex]\[
\text{Mass} = 10.5 \text{ cubic meters} \times 1000 \text{ kg/m}^3 = 10500 \text{ kg}
\][/tex]
3. Calculate the Force of Gravity:
The force of gravity can be calculated using Newton's second law of motion (Force = Mass × Acceleration). Here, the acceleration due to gravity (g) is 9.81 m/s². The formula for the force of gravity is:
[tex]\[
\text{Force\_gravity} = \text{Mass} \times \text{Gravity}
\][/tex]
Given:
- Mass = 10500 kg
- Gravity = 9.81 m/s²
Substituting the values:
[tex]\[
\text{Force\_gravity} = 10500 \text{ kg} \times 9.81 \text{ m/s}^2 = 103005 \text{ N}
\][/tex]
Thus, the force of gravity acting on the column of water is [tex]\( 103005 \text{ N} \)[/tex].
Reviewing the given options:
A) 68,600 N
B) 102,900 N
C) 73,500 N
D) 110,700 N
It is clear that none is exactly [tex]\( 103005 \text{ N} \)[/tex], but the closest is option B) [tex]\( 102,900 \text{ N} \)[/tex].
Therefore, the answer is:
B) [tex]\( 102,900 \text{ N} \)[/tex]
