Question

A piece of iron of density 7.8 × 10^-3 kg/m³ and  volume 100 cm³ is totally immersed in the water, then upthrust is(density of water 1000 kg/m³)
1. 1 N
2. 10 N
3. 100 N
4. 1000 N

Answer 1

Correct Answer - Option 1 : 1 N

CONCEPT:

• Archimedes' principle:It 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.
• When an object is submerged in fluid fully or partially there are two forces,
  • 1. buoyant force: an upward force is exerted on the body. 
  • 2. weight of the object 

Formula for buoyant force is:

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, and g is the gravitational acceleration.

Formula for weight of the object:

 W = mg = ρo Vo g  

where ρo is the density of the object, Vo is the volume of the object, g is the gravitational acceleration.

EXPLANATION:

Given that,ρ = density of liquid (here water) = 1000 kg/m³, V = volume of immersed object or displaced liquid = 100 x 10^-6 m³

now, the upthrust is given as

F = ρ × g × V

F = 1000 x 9.81 x 100 x 10^-6 m³

F = 0.98 N 

Approximately 1 N,

So, the correct option is 1 N