Question

we know that force of buoyancy=weight of body in air - weight of body in water. then force of bouyancy = weight of the body in water.
can you please explain what this actually mean

Answer 1

Heya friend, Have you ever dropped your swimming goggles in the deepest part of the pool and tried to swim down to get them? It can be frustrating because the water tries to push you back up to the surface as you're swimming downward. The name of this upward force exerted on objects submerged in fluids is called the buoyant force.
So why do fluids exert an upward buoyant force on submerged objects? It has to do with differences in pressure between the bottom of the submerged object and the top. Say someone dropped a can of beans in a pool of water. Not again!

Because pressure (P_{gauge}=\rho gh)(P
​gauge
​​ =ρgh)left parenthesis, P, start subscript, g, a, u, g, e, end subscript, equals, rho, g, h, right parenthesis increases as you go deeper in a fluid, the force from pressure exerted downward on the top of the can of beans will be less than the force from pressure exerted upward on the bottom of the can.
Essentially it's that simple. The reason there's a buoyant force is because of the rather unavoidable fact that the bottom (i.e. more submerged part) of an object is always deeper in a fluid than the top of the object. This means the upward force from water has to be greater than the downward force from water.