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A block of mass m and density d is immersed into the liquid completely. Find apparent loss in weight of block if density of liquid is D.
1. \( {mgD \over d}\)
2. \( {mgd \over D}\)
3. \( {d \over mgD}\)
4. mg

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Correct Answer - Option 1 : \( {mgD \over d}\)

CONCEPT:

  • Archimedes' principle: When a body is submerged in a fluid, whether fully or partially submerged, the upward buoyant force that is exerted on it, is equal to the weight of the fluid that the body displaces when it is inside the fluid.
  • Buoyant force: When an object is immersed in fluid fully or partially, an upward force is exerted on the body by the fluid. This force is known as the buoyant force. 

Fbuoyant = ρVf g 

where ρf is the density of the fluid in which the object is submerged, Vf is the volume of the displaced fluid (or volume of the object that is submerged inside the fluid partially or fully)  and g is the gravitational acceleration.

  • The apparent loss of weight in an object, when submerged, is equal to the buoyant force.

CALCULATION:

Given that the Density of liquid = D, density of block = d, the mass of block = m

The volume of liquid displaced = volume of block = mass of block/density of a block

Volume of liquid displaced (V) = m/d

We know that Apparent loss of weight = Buoyant force

The apparent loss of weight of metal = W = density of liquid × Volume of liquid displaced × g

W = D V g = D (m/d) g

\(Apparent ~loss = {mgD \over d}\)

So the correct answer is option 1. 

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