Question

A piece of metal of mass 1 Kg is completely immersed in water. The water level rises by 100 ml. Calculate apparent loss of weight in the metal. (given density of water = 1000 g/cc and g = 9.8 m/s²)
1. 0.00098 N
2. 1 N
3. 9.8 N
4. 0.098 N

Answer 1

Correct Answer - Option 1 : 0.00098 N

CONCEPT:

• Archimedes' principle states that when a body immersed 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.
• Buoyant force: When an object is submerged in fluid fully or partially, an upward force is exerted on the body. This force is known as the buoyant force. 

​Fbuoyant = ρf Vf 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)  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 water ρw = 1000 g/cc = 1 kg/m³ and g = 9.8 m/s2 

The volume displaced Vw = 100 ml = 10^-4 m³

We know that Apparent loss of weight = Buoyant force

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

W = ρwVw g 

W = 1 kg/m3 × 10-4 m3 × 9.8 m/s2 

W = 0.00098 N

So the correct answer is option 1.