When a body lighter than water is completely submerged in water , the ...
Concept: Laws of flotation. Let m be the mass of a body, thenweight of the body = mglet σ is the density of the object and ρ is the density of the water, V is the volume of the object.weight = mg = Vσgbuoyant force = Vρg ( due to liquid)buoyant force=n×weight( given)= Vρg=nVσg= σ /ρ = 1/n. ( Specific gravity = density of object /density of water.) Hence, answer is 1/n.
When a body lighter than water is completely submerged in water , the ...
Buoyancy Force and Weight of the Body
Buoyancy force is the upward force exerted on an object submerged in a fluid, which opposes the weight of the object. In this scenario, the body is lighter than water, so it floats when submerged.
1. Weight of the Body:
The weight of an object is the force acting on it due to gravity. It can be calculated using the formula:
Weight = mass * acceleration due to gravity
W = mg
2. Buoyancy Force:
The buoyancy force is equal to the weight of the fluid displaced by the object. It can be calculated using Archimedes' principle:
Buoyancy force = weight of the fluid displaced
Fb = ρVg
where ρ is the density of the fluid, V is the volume of fluid displaced, and g is the acceleration due to gravity.
Buoyancy Force in terms of Specific Gravity
1. Specific Gravity:
Specific gravity is the ratio of the density of a substance to the density of a reference substance (usually water). Mathematically, it is expressed as:
Specific gravity = density of substance / density of water
2. Relationship between Specific Gravity and Buoyancy Force:
The buoyancy force acting on a body depends on the volume of fluid displaced, which is related to the specific gravity of the material of the body.
When a body is completely submerged in water and the buoyancy force acting on it is found to be n times its weight, we can use the following relationship:
Buoyancy force = Specific gravity * weight of the body
Substituting the given values:
n * weight = Specific gravity * weight
Simplifying the equation:
Specific gravity = n
Therefore, the specific gravity of the material of the body is equal to n.
Answer: The specific gravity of the material of the body is 1/n.
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