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Buoyant force

What is buoyant force? I’m unable to understand practically from book. please give vast and practical explanation.. (Raj asked)

Whenever a body is immersed in a fluid, say water, it experiences an upward force acting on it. The upward force exerted by a fluid on an object immersed in it is called Buoyant force.

When an object is immersed, it displaces the fluid already present there. The upward force (buoyant force) is the result of the fluid’s attempt to reoccupy the space.

If the object placed in a fluid is denser than the fluid, it will sink. Though it experiences an upthrust, its weight will be more than the upthrust.

The upthrust is equal to the weight of liquid displaced by the immersed part of the body.

If the object is of less density than the fluid, it will come up and float.

For a floating body, the net weight is equal to zero, as the upthrust balances the actual weight of the body.

Motion under gravity

Two stones of mass 5 kg and 10 kg are dropped from the same height above the ground level. Which one will hit the ground first? Why?

Answer: Both the stones will reach the ground simultaneously (provided we neglect the air resistance (the viscosity) and buoyant force.

This is because acceleration due to gravity is independent of mass of the freely falling body.

A problem from Hydraulic

“a stone of [wiki]density [/wiki] 4gm/cm3 is dropped freely in a liquid of density 0.8 gm/cm3 .what will be the acceleration of the sinking stone?”

Ans:

the force acting are

weight =mg= $\frac{4}{3}\pi r^{3}\rho g$ downwards (where $\rho$ is the density of the body)

[wiki]Buoyant force[/wiki] =$\frac{4}{3}\pi r^{3}\sigma g$

SO, THE NET DOWNWARD [wiki]FORCE [/wiki]IS
$\frac{4}{3}\pi r^{3}(\rho -\sigma ) g$

Therefore, acceleration = net downward force / mass

=$\frac{\frac{4}{3}\pi r^{3}(\rho -\sigma ) g}{\frac{4}{3}\pi r^{3}\rho }$
=$\left (1-\frac{\sigma }{\rho } \right )g$

Now substitute the values and calculate