A spherical solid ball of volume V is made of a material of density ρ_{1}. It is falling through a liquid of density ρ_{2}(ρ_{2} <ρ_{1}). Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed v, i.e., Fviscous = −kv^{2} (k>0). The terminal speed of the ball is
A.
ρ_{1}Vg − ρ_{2}Vg = kv_{2}^{T}
Water is flowing continuously from a tap having an internal diameter 8 × 10^{-3} m. The water velocity as it leaves the tap is 0.4 ms^{-1}. The diameter of the water stream at a distance 2 × 10^{-1} m below the tap is close
to:
7.5 x 10^{-3} m
9.6x 10^{-3} m
3.6x 10^{-3} m
5.0x 10^{-3} m
C.
3.6x 10^{-3} m
From Bernoulli's theorem
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?
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 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
D.
20 cm
Water will rise to the full length of capillary tube
A jar filled with two non-mixing liquids 1 and 2 having densities ρ_{1} and ρ_{2} respectively. A solid ball, made of a material of density ρ_{3}, is dropped in the jar. It comes to equilibrium in the position shown in the figure.
Which of the following is true for ρ_{1}, ρ_{2} and ρ_{3}?
ρ_{3} < ρ_{1} < ρ_{2}
ρ_{1} < ρ_{3} < ρ_{2}
ρ_{1} < ρ_{2} < ρ_{3}
ρ_{1} < ρ_{3} < ρ_{2}
D.
ρ_{1} < ρ_{3} < ρ_{2}
As liquid 1 floats above liquid 2,
ρ_{1} < ρ_{2}
The ball is unable to sink into liquid 2, ρ_{3} < ρ_{2}
The ball is unable to rise over liquid 1
ρ_{1} < ρ_{3} Thus, ρ_{1} < ρ_{3} < ρ_{2}
Spherical balls of radius R are falling in a viscous fluid of viscosity η with a velocity v. The retarding viscous force acting on the spherical ball is
directly proportional to R but inversely proportional to v.
directly proportional to both radius R and velocity v.
inversely proportional to both radius R and velocity v.
inversely proportional to R but directly proportional to velocity v.
B.
directly proportional to both radius R and velocity v.
Retarding force acting on a ball falling into a viscous fluid
F = 6πηRv
where R = radius of the ball
v = velocity of ball and
η = coefficient of viscosity
∴ F ∝ R and F ∝ v
Or in words, retarding force is proportional to both R and v
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?
C.
Capillary rise h = 2T cosθ /ρgr. As soap solution has lower T, h will be low.
If two soap bubbles of different radii are connected by a tube,
air flows from the bigger bubble to the smaller bubble till the sizes are interchanged.
air flows from bigger bubble to the smaller bubble till the sizes are interchanged
air flows from the smaller bubble to the bigger.
there is no flow of air.
C.
air flows from the smaller bubble to the bigger.
The excess pressure inside the soap bubble is inversely proportional to the radius of soap bubble i.e. P ∝1/r, r being the radius of the bubble. It follows that pressure inside a smaller bubble is greater than that inside a bigger bubble. Thus, if these two bubbles are connected by a tube, air will flow from smaller bubble to bigger bubble and the bigger bubble grows at the expense of the smaller one.
There is a circular tube in a vertical plane. Two liquids which do not mix and of densities d_{1} and d_{2} are filled in the tube. Each liquid subtends 90^{o} angle at centre. Radius joining their interface makes an angle α with vertical. ratio d_{1}/d_{2} is
C.
If the terminal speed of a sphere of gold (density = 19.5 kg/m3 ) is 0.2 m/s in a viscous liquid (density = 1.5 kg/m3 ) of the same size in the same liquid.
0.2 m/s
0.4 m/s
0.133 m/s
0.1m/s
D.
0.1m/s