Mechanical properties of fluids practice · Mixed difficulty

Select the correct statements from the following.

A body of density $\rho$ is dropped from rest from height $h$ (from the surface of water) into a lake of density of water $\sigma(\sigma>\rho)$. Neglecting all dissipative effects, the acceleration of body while it is in the lake is

A cubical block of steel of each side equal to $l$ is floating on mercury in a vessel. The densities of steel and mercury are $\rho_s$ and $\rho_m$. The height of the block above the mercury level is given by

A ball whose density is$0.4 \times {10^3}\mathrm{kg}{\mathrm{m}^{ - 3}}$ falls into water from a height of 9 cm. To what depth does the ball sink?

A boat having a length $3 \mathrm{~m}$ and breadth $2 \mathrm{~m}$ is floating on a lake. The boat sinks by $1 \mathrm{~cm}$ when a man gets on it. The mass of the man is

A sample of metal weight $300 \mathrm{~gm}$ in air, $270 \mathrm{~gm}$ liquid. Then find:

(1) Relative density of metal

(2) Relative density of unknown liquid.

The pressure on a swimmer 20 m below the surface of water at sea level is

Three capillaries of lengths $l, 2 l$ and $l / 2$ are connected in series. Their radii are $r, r / 2$ and $r / 3$ respectively. If stream-line flow is maintained and the pressure difference across the first capillary tube is $p_1$, find the pressure difference across (i) the second and (ii) the third capillary tube.

A body is floating in liquid with $50 \%$ of its volume outside the liquid. When the entire system accelerates upwards with an acceleration $g / 3$, the percentage of its volume outside the liquid is

Correct Bernoulli's equation is (symbols have their usual meaning) :

A solid shell loses half of its weight in water. If relative density of shell is 5 , then what fraction of its volume is hollow?

The reading of spring balance when a block is suspended from it in air is 60N. This reading is changed to 40N when the block is submerged in water. The specific gravity of the block must therefore

What is the pressure inside a vapour bubble of radius $10^{-3} \mathrm{~m}$ formed in boiling water? Surface tension of water at 100 is $0.059 \mathrm{~Nm}^{-1}$ and $1 \mathrm{~atm}=101325 \mathrm{~Nm}^{-2}$.

Angle of contact of a liquid with a solid depend on

A metal ball weighs $0.096 \mathrm{~N}$. When suspended in water it has an apparent weight of $0.071 \mathrm{~N}$. Find the density of the metal.

If a soap bubble expands, the pressure inside the bubble:

Check the dimensional consistency of the Poiseuille's formula for the laminar flow in a tube: $Q=\frac{\pi R^4\left(p_1-p_2\right)}{8 \eta l}$

Given below are two statements: one is labelled as
Assertion A and the other is labelled as Reason R

Assertion A : A spherical body of radius $\left( {5 \pm 0.1} \right)\,\,{\text{mm}}$ having a particular density is falling through a
liquid of constant density. The percentage error in
the calculation of its terminal velocity is 4%.

Reason R : The terminal velocity of the spherical
body falling through the liquid is inversely
proportional to its radius.

In the light of the above statements, choose the
correct answer from the options given below

Assertion: The upper surface of the wings of an aeroplane is made convex and the lower surface is made concave.
Reason: The air currents at the top have a smaller velocity and thus less pressure at the bottom than at the top.

The working of venturimeter is based on

A: A hydrogen filled balloon stops raising after it has attained a certain height in the sky
R: The buoyancy of an object depends both on the material and shape of the object

If $\rho$ is the density and $\eta$ is coefficient of viscosity of fluid which flows with a speed $v$ in the pipe of diameter $d,$ the correct formula for Reynolds number ${R_e}$ is:

Eight small raindrops each of radius $1 {~mm}$, come down with a terminal velocity of $10 {~cm} / {s}$. They coalesce to form a bigger drop. The terminal velocity of the bigger drop will be

Which of the following is not the unit of surface tension?

Assertion: The flow of fluid is said to be steady if at any given point, the velocity of each passing fluid particle do not remain constant.
Reason: The path taken by a fluid particle under a steady flow is a turbulent.

Two solids $A$ and $B$ float in water. It is observed that A floats with$\frac{1}{2}$ of its body immersed in water and $B$ floats with $\frac{1}{4}$ of its volume above the water level. The ratio of the density of $A$ to that of $B$is

If a large drop of radius $2 \mathrm{~cm}$ is splitted into 8 identical small droplets. Find out work done in this process if surface tension of liquid is $\mathrm{T ~dyne}/ \mathrm{cm}$.

Statement-1: Coefficient of viscosity of a liquid decreases while that of a gas increase, with increasing temperature.
Statement-2: Density of a liquid and that of a gas vary in opposite manner with increase in temperature.

Assertion: It is better to wash the clothes in hot soap solution.
Reason: The surface tension of cold solution is more than the surface tension of hot solution.

Equal mass of three liquids are kept in three identical cylindrical vessels A, B and C. Their densities are $\rho_A, \rho_B, \rho_C$ with $\rho_A<\rho_B<\rho_C$. The force on the base will be