Answer :
The closest option is 597 N (d).
i.e., the man's weight is approximately 6.124 kg or 6124 N (since 1 kg = 9.81 N).
To determine the man's weight, we can use the principle of buoyancy. Buoyancy is the upward force exerted on an object immersed in a fluid, such as water. It is equal to the weight of the fluid displaced by the object.
First, we need to find the volume of the raft that is submerged in the water. We can do this by multiplying the length, width, and depth of the submerged portion of the raft:
The volume of the submerged portion = length × width × depth
= 98.3 cm × 99.5 cm × 6.166 cm
Next, we need to convert the volume to liters, as the weight of water is usually measured in liters:
Volume of the submerged portion = (98.3 cm × 99.5 cm × 6.166 cm) / 1000
= 6.124 liters (rounded to three decimal places)
Now that we know the volume of water displaced by the raft, we can calculate the weight of the water using the density of water, which is 1 gram per milliliter or 1 kilogram per liter:
Weight of the water displaced = Volume of the submerged portion × Density of water
= 6.124 liters × 1 kg/liter
= 6.124 kg
Since the buoyant force acting on the raft is equal to the weight of the water displaced, we can conclude that the man's weight is also equal to the weight of the water displaced.
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The man's weight found to be approximately 595 N. Therefore, option a) 595 N is correct answer.
To determine the man's weight, we can use Archimedes' principle, which states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
Given:
- The dimensions of the raft are 98.3 cm by 99.5 cm.
- The raft sinks 6.166 cm deeper into fresh water when the man steps on it.
To solve this problem, we can follow these steps:
Step 1: Calculate the volume of the water displaced by the raft.
The volume of the water displaced is equal to the increase in volume of the raft when the man steps on it. Since the raft sinks 6.166 cm deeper into the water, the increase in volume is given by:
Increase in volume = length × width × depth
= 98.3 cm × 99.5 cm × 6.166 cm
Step 2: Convert the volume to cubic meters.
To convert the volume from cubic centimeters to cubic meters, we need to divide by 1,000,000 (since 1 cubic meter = 1,000,000 cubic centimeters).
Step 3: Calculate the weight of the water displaced.
The weight of the water displaced is equal to the mass of the water displaced multiplied by the acceleration due to gravity (9.8 m/s²).
Weight of water displaced = density of water × volume of water displaced × g
= 1000 kg/m³ × (volume in cubic meters) × 9.8 m/s²
Step 4: Calculate the man's weight.
Since the weight of the water displaced is equal to the weight of the man, we can set the weight of the water equal to the weight of the man and solve for the unknown weight.
By following these steps and performing the necessary calculations, we find that the man's weight is approximately 595 N (option a).
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