The balloon filled with hydrogen is rising because the weight of the balloon filled with hydrogen is less than the weight of air displaced by it i.e. upthrust of the atmosphere is acting on the balloon. As we go up in the atmosphere the density of air decreases that leads to decrease in the weight of displaced air i.e. decrease in the upthrust. As the weight of the hydrogen balloon is same to the weight of air displaced by it, it stops to rise.

Specific density of iron is higher than that of water and less then that of mercury. Being denser than water it sinks in water but is less denser than mercury so it floats in mercury.
The upthrust provided by a medium is directly proportional to the density of the medium i.e. more the density more is the upthrust. Water is denser than air so upthrust provided by water is higher than that of air. So , having more upthrust in water means the object looses some of its weight than in air. So, due to that loss in the weight, the object is lighter in water than in air.
The upthrust provided by a medium is directly proportional to the density of the medium i.e. more the density more is the upthrust. Water is denser than air so upthrust provided by water is higher than that of air. So, we are getting extra lift from below when the object is in water than it was in air. So, due to that extra push a person can lift a heavy stone immersed in water easily as compaired to air .
The density of salty water is higher than that of pure water and according to upthrust formula medium having higher density will provide higher upthrust (Upthrust is directly proportional to the density of the medium). So, salt water will push the swimmer body upward with more force than that of pure water. Due to that extra push by salty water it is easier to swim in salty water than in pure water.
Archimedes' principle states that, "When an object is fully or partially immersed in liquid substance, the weight of the displaced liquid is equal to the upthrust of the liquid on the object".
"An object that floats on a liquid medium displaces the liquid equal to its weight".
According to anamolous behavior of water, ice floats in water because its density is lower thatn that of water

Given,

Density of wood(d1)= 800kg/m3

Density of water (d2)=100kg/m3

Volume of wood(V)=1.6m3

Mass of wood (m)= d1×v

=800×1.6

=1280kg

Now,

Mass of displaced water=mass of wood=1280kg

\begin{align*} \text{Volume of wood, sinking on water}&= \text{volume of displaced water} \\&=\frac{\text{mass of displaced water} }{\text{density of water}}\\ &= \frac{1280kg}{1000kg/m^3}\\ &= 1.28 \: m^3\end{align*}

\begin{align*}\text{Sinking part of wood} &= \frac{\text{Volume of wood sinking on water}}{\text{Volume of wood}}\\ &=\frac{1.28m^3}{1.6m^3}\\&= 0.8 \end{align*}

Here,mass of a brick(m1) = 2 kg

Density of the brick (d1) = 2.5 g/cm3 = \(\frac {2.5 × 10^{-3} kg}{10^{-6} m^3}\)

= 2500 kg/m3

∴ Volume of the brick (V1) = \(\frac{mass}{density}\)

= \(\frac{2}{2500}\)

∴ Mass of the displaced water is 0.8 kg.

= \(\frac{1}{1250}\)m3

Here,mass of brick (m1) = 2 kg

Density of brick(d1) = 2.5g /cm3

= 2500 kg/m3

Density of water (d2) = 1000 kg/m

Mass of water displaced = (m2) = ?

For sinking bodies

V1=V2

or, \(\frac{m_1}{d_1}\)=\(\frac{m_2}{d_2}\) [∴d=\(\frac{m}{v}\) ]

∴ \(\frac{d_1}{d_2}\)=\(\frac{m_1}{m_2}\)

\(\frac{2500}{1000}\)

\(\frac{2}{m_2}\)

∴ m2 =\(\frac{1000×2}{2500}\)

= \(\frac{20}{25}\)

= \(\frac{4}{5}\)

= 0.8 kg

∴ Mass of the displaced water is 0.8 kg.

Pascal's law states that liquid exerts pressure equally in all directions.

Given,

Depth of water (h) = 6m

Density of water (d) =1000 kg /m3

Acceleration due to gravity (g) = 9.8/sec2

Pressure of water (p) =?

We know,

p=h× d× g

=6 × 1000×9.8

=58800Pa

Hence, the water pressure exerted at the bottom of the tank is 58800 Pascal.