An iron piece of mass 360g and a density of 6g/cm if suspended by a rope so that is partially submerged in oil of density 0.9g/cm find the tension (force) in the string
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To find the tension in the string, we need to consider the forces acting on the iron piece.
Let's break it down step by step:
1. Calculate the volume of the iron piece:
The volume can be found using the formula:
volume = mass / density
In this case, the mass of the iron piece is 360g, and the density is 6g/cm.
So, volume = 360g / 6g/cm = 60 cm³
2. Determine the submerged volume:
Since the iron piece is partially submerged in oil, we need to find the volume of the portion submerged in oil.
The density of the oil is given as 0.9g/cm³.
Therefore, the submerged volume can be calculated using the formula:
submerged volume = total volume * (density of iron / density of oil)
submerged volume = 60 cm³ * (6g/cm³ / 0.9g/cm³) = 400 cm³
3. Calculate the buoyant force:
The buoyant force is the force exerted by the fluid on the submerged object and equals the weight of the fluid displaced by the object.
The buoyant force can be found using the formula:
buoyant force = density of fluid * volume of fluid displaced * acceleration due to gravity
Here, the density of the fluid (oil) is given as 0.9g/cm³, the volume of fluid displaced is 400 cm³, and the acceleration due to gravity is approximately 9.8 m/s².
First, convert the volume of fluid displaced to liters (divide by 1000): 400 cm³ / 1000 = 0.4 liters
Then, calculate the buoyant force:
buoyant force = 0.9g/cm³ * 0.4 liters * 9.8 m/s² = 3.528 N
4. Determine the tension in the string:
The tension in the string can be found by balancing the forces acting on the iron piece. In this case, the forces are gravity (weight) and the buoyant force.
The weight of the iron piece can be calculated using the formula:
weight = mass * acceleration due to gravity
weight = 360g * 9.8 m/s² = 3.528 N (same as the buoyant force)
Since the weight and the buoyant force are equal, the tension in the string will be the same as the weight, which is 3.528 N.
Therefore, the tension (force) in the string is 3.528 N.