A 20 cm long capillary tube is dipped in water. The water rises up to 8 cm. If the entire arrangement is put in a freely falling elevator the length of water column in the capillary tube will be

• 8 cm

• 10 cm

• 4 cm

• 20 cm

A ball is made of a material of density ρ where ρ_oil < ρ < ρ_water with ρ_oil and ρ_water representing the densities of oil and water, respectively. The oil and water are immiscible. If the above ball is in equilibrium in a mixture of this oil and water, which of the following pictures represents its equilibrium position?

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C.

 ρ_oil < ρ < ρ_water 
Oil is the least dense of them, so it should settle at the top with water at the base. Now, the ball is denser than oil but less denser than water. So, it will sink through oil but will not sink in water. So, it will stay at the oil -water interface.

A capillary tube (A) is dropped in water. Another identical tube (B) is dipped in a soap water solution.Which of the following shows the relative nature of the liquid columns in the two tubes? 

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C.

Capillary rise h = 2T cosθ /ρgr. As soap solution has lower T, h will be low. 

A jar filled with two non-mixing liquids 1 and 2 having densities ρ₁ and ρ₂ respectively. A solid ball, made of a material of density ρ₃, is dropped in the jar. It comes to equilibrium in the position shown in the figure.
Which of the following is true for ρ₁, ρ₂ and ρ₃?

• ρ₃ < ρ₁ < ρ₂

• ρ₁ < ρ₃ < ρ₂

• ρ₁ < ρ₂ < ρ₃

• ρ₁ < ρ₃ < ρ₂

D.

ρ₁ < ρ₃ < ρ₂

As liquid 1 floats above liquid 2,
ρ₁ < ρ₂
The ball is unable to sink into liquid 2, ρ₃ < ρ₂
The ball is unable to rise over liquid 1
ρ₁ < ρ₃ Thus, ρ₁ < ρ₃ < ρ₂

A spherical solid ball of volume V is made of a material of density ρ₁. It is falling through a liquid of density ρ₂(ρ₂ <ρ₁). Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed v, i.e., Fviscous = −kv² (k>0). The terminal speed of the ball is

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A.

ρ₁Vg − ρ₂Vg = kv₂^T