50 ml of water in a beaker will exert what pressure on the beaker than 50ml of water in a 350ml beaker
To determine the pressure exerted by the water in each beaker, we need to consider the concept of pressure and the equation relating pressure, force, and area.
Pressure (P) is defined as the force (F) per unit area (A). Mathematically, it can be expressed as:
P = F / A
In this case, the force is the weight of the water, which can be calculated using the formula:
F = m * g
where m represents the mass of the water and g is the acceleration due to gravity. Since we are dealing with the same volume of water (50 ml) in both beakers, the mass will also be the same in both cases. Therefore, the force will be the same.
Now, let's consider the area (A). The area is the bottom surface area of the beaker in contact with the water. Since the beaker's size is different in each case, the area will also vary.
To calculate the pressure, we need to divide the same force (weight of the water) by the respective areas of the beakers. Assuming the beaker's bottom surface area is proportional to the volume, we can calculate the pressure ratio as:
Pressure ratio = (Area of 50ml beaker / Area of 350ml beaker)
To find out the exact pressure ratio, we need more information about the shapes and dimensions of the beakers. However, assuming the beakers are similar in shape, we can use the ratio of their volumes to estimate the ratio of their areas.
The volume ratio is:
Volume ratio = 50 ml / 350 ml
Assuming the beakers are similar, we can consider them as scaled versions of each other. In such a case, the volume is proportional to the cube of a linear dimension, and the area is proportional to the square of this dimension.
Let's assume the scaling factor between the two beakers is x. Therefore, we have the following relationships:
(50 ml / 350 ml) = (x^3 / 1)
(x^3) = (50 / 350)
x ≈ 0.535
Therefore, the linear dimensions of the 350 ml beaker would be approximately 0.535 times the linear dimensions of the 50 ml beaker.
Since the area is proportional to the square of the linear dimensions, the area ratio would be:
Area ratio = (0.535^2) ≈ 0.286
This means that the area of the bottom of the 350 ml beaker is approximately 0.286 times the area of the bottom of the 50 ml beaker.
Hence, the pressure exerted by the 50 ml of water in the larger 350 ml beaker is around 0.286 times the pressure exerted by the same volume of water in the smaller 50 ml beaker.