Physics

Fluid Mechanics

637 Questions

Fluid mechanics is a core physics topic that evaluates the principles of liquid pressure, buoyancy, density, and viscosity through complex numerical problems. The questions require calculating the volume of submerged objects, understanding hydraulic jumps, and applying fundamental fluid statics principles. It is a highly scoring subject for candidates preparing for technical and engineering competitive exams.

Liquid pressure and depthBuoyancy and densityVolume expansionHydraulic jump calculationsSurface tension mechanics

Fluid Mechanics Questions

Multiple choice physics simple harmonic motion a few applications of linear shm simple pendulum example of simple harmonic motion

A solid cube of side $a$ and density $\rho _{0}$ floats on the surface of a liquid of density $\rho $. If the cube is slightly pushed downward, then it oscillates simple harmonically with a period of:

  1. $\displaystyle 2\pi \sqrt{\frac{\rho _{0}}{\rho }\frac{a}{g}}$
  2. $\displaystyle 2\pi \sqrt{\frac{\rho }{\rho _{0}}\frac{a}{g}}$
  3. $\displaystyle 2\pi \sqrt{\frac{a}{\left ( 1-\frac{\rho }{\rho _{0}} \right )g}}$
  4. $\displaystyle 2\pi \sqrt{\frac{a}{\left ( 1+\frac{\rho }{\rho _{0}} \right )g}}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\displaystyle T=2\pi \sqrt{\frac{m}{k}}$
Here Mass of the cube is $m=\left ( \rho _{0} \right )\left ( a^{3} \right )$
Since the cube is pushed very slightly so the part dipped into the water is very negligible 

Spring constant for a negligible distance  $k=\rho _{1} \times $  bottom surface area of cube $\times g=\rho a^{2}g$
$\therefore $   $\displaystyle T=2\pi \sqrt{\frac{\rho _{0}a}{\rho g}}$

Multiple choice physics simple harmonic motion a few applications of linear shm simple pendulum example of simple harmonic motion

A small ball of density $\rho _{0}$ is released from rest from the surface of a liquid whose density varies with depth $h$ as $\rho =\dfrac{\rho _{0}}{2}(a+\beta h)$Mass of the ball is $m$.Select the most appropriate option:

  1. The particle will execute SHM.
  2. The maximum speed of the ball is $\dfrac{2-a}{\sqrt{2\beta }} $.

  3. Both (a) and (b) are correct.

  4. Both (a) and (b) are wrong.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
$\rho = \dfrac {\rho _{o}}{2} (a + \beta h)$
$V = \dfrac{m}{\rho _{o}}$
Downward force, $F = mg - \dfrac{m}{\rho _{o}}\dfrac{\rho _{o}}{2}(a+\beta h)g$
$F = mg\left ( \left ( 1- \dfrac{a}{2} \right )- \dfrac{\beta h}{2}\right )$
So F is proportional to displacement from center position which is $mg (1 - \dfrac{a}{2})$ below surface
Therefore, the motion is SHM.
A = $mg (1 - \dfrac{a}{2})$
$k = \dfrac{mg \beta}{2}$
Also, $k = m\omega^{2}$
=> $\omega = \sqrt{\dfrac{g\beta}{2}}$
$v _{max} = \omega A = \dfrac{(2-a) \sqrt{g}}{\sqrt{2} \beta}$
Answer A
Multiple choice various types of barometer fluids physics

Mercury is the heaviest liquid.
What is the advantage of the given property in the working of a barometer?

  1. It gives stability to the apparatus.

  2. Its rises to a maximum height of 76 cm which is the smallest value for a fluid.

  3. Other impurities float over it.

  4. It is poisonous.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Since the density of mercury is highest in the liquids, it needs smallest column to measure the pressure reducing the size of the equipment and making it easier to use. 

Multiple choice various types of barometer fluids physics

An aluminum can of cylindrical shape contains $V _{0}\ cm^{3}$ of water. The area of the linear cross-section of the can is $A _{0}\ cm^{2}$. (All measurement refer to $T _{0}^\circ C$). Find the rise in the water level, if the temperature increases to $T _{1}C(T _{1}^\circ C > T _{0}$) $\alpha _{Al}$ and $\gamma _{water}$ are given

  1. $\dfrac { { V } _{ 0 }\left( { T } _{ 1 }-{ T } _{ 0 } \right) \left( { \gamma } _{ w }-2{ \alpha } _{ Al } \right) }{ { A } _{ 0 } } $
  2. $\dfrac { { V } _{ 0 }\left( { T } _{ 1 }-{ T } _{ 0 } \right) \left( { \gamma } _{ w }-2{ \alpha } _{ Al } \right) }{ {2A } _{ 0 } } $
  3. $\dfrac { { V } _{ 0 }\left( { T } _{ 1 }-{ T } _{ 0 } \right) \left( { \gamma } _{ w }-2{ 3\alpha } _{ Al } \right) }{ { A } _{ 0 } } $
  4. $\dfrac { { V } _{ 0 }\left( { T } _{ 1 }-{ T } _{ 0 } \right) \left( { \gamma } _{ w }-2{ 3\alpha } _{ Al } \right) }{ { 2A } _{ 0 } } $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The volume of water at T1 is V1 = V0(1 + gamma_w * dT). The area of the can at T1 is A1 = A0(1 + 2 * alpha_Al * dT). The new height h1 = V1 / A1. The rise in level is h1 - h0 = (V0/A0) * [(1 + gamma_w * dT) / (1 + 2 * alpha_Al * dT) - 1]. Using binomial approximation (1+x)^-1 approx 1-x, this simplifies to (V0/A0) * dT * (gamma_w - 2 * alpha_Al).

Multiple choice various types of barometer fluids physics

In the bottom of a vessel with mercury of density $\rho$ there is a round hole of radius $r$. At what maximum height of the mercury layer will the liquid still not flow out through this hole. (Surface tension = $T$) 

  1. $\dfrac T {rpg}$
  2. $\dfrac T {2rpg}$
  3. $\dfrac {2T} {rpg}$
  4. $\dfrac{4T} {rpg}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given,


$r=$ radius of the hole


$p=$ density of mercury liquid

$g=$ acceleration due to gravity

$T=$ Surface tension

$h=$ maximum height

The liquid can not penetrate until the hydro-static pressure is greater than excess pressure.

Limiting condition,

$pgh=\dfrac{2T}{r}$

$h=\dfrac{2T}{rpg}$

The correct option is C.

Multiple choice various types of barometer fluids physics

A cubical block of steel of each side equal 1 is floating on mercury in 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 

  1. $ I \left( 1+\dfrac { \rho _ s }{ \rho _ m } \right) $
  2. $ I \left( 1-\dfrac { \rho _ s }{ \rho _ m } \right) $
  3. $ I \left( 1+\dfrac { \rho _ m }{ \rho _ s } \right) $
  4. $ I \left( 1-\dfrac { \rho _ m }{ \rho _ s} \right) $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

By Archimedes' principle, the weight of the block equals the weight of the displaced mercury. rho_s * L^3 * g = rho_m * (L^2 * (L-h)) * g, where h is the height above the surface. rho_s * L = rho_m * (L-h). L - h = L * (rho_s / rho_m). h = L * (1 - rho_s / rho_m).

Multiple choice various types of barometer fluids physics

A beaker contining a liquid is kept inside a big closed jar. If the air inside the jar is continuously pumped out, the pressure in the liquid near the bottom of the liquid will

  1. Increase

  2. Decrease

  3. Remain constant

  4. First decrease and then increase
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The pressure at depth h in a liquid is P = P_atm + rho * g * h. If the air is pumped out, P_atm decreases, so the total pressure at any depth h also decreases.

Multiple choice chemistry properties of natural resources conservation of water and recycling properties of water structure and properties of water

The density of water is:

  1. $1\ g/cm$$^3$
  2. $20\ g/cm$$^3$
  3. $2\ g/cm$$^3$
  4. $0.1\ g/cm$$^3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The density of water is $1 g/cm^{3}$. Density is a ratio of Mass to the Volume. 1 meter long, 1 meter wide, 1 meter high storage tank can store 1,000 kg mass of water. So the density of water is 1. Therefore 1 kg water= 1 litre water(approximately).

Multiple choice chemistry properties of natural resources conservation of water and recycling properties of water structure and properties of water

The density of water at  $0^{\circ} C $ is less than the density of water at $ 4^{\circ}C $.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The density of water at $0^oC$ is less than the density of water at $4^oC$. When water is heated from $0^oC$ its volume decreases because its density increase we can see this effect up to $4^oC$, afterward density decreases.

Multiple choice chemistry properties of natural resources conservation of water and recycling properties of water structure and properties of water

At 4$^{\circ}$C, water starts expanding and continues to do so till 0$^{\circ}$C.

Is the above statement correct?

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

When water is heated from $0^oC$ its value decreases because its density increases and we can see this effect up to $4^oC$ because the density of ice is maximum at $4^oC$. Afterward the density decreases, the volume increases.

As, when we cool it from $4^oC$ its volume increases up to $0^oC$. At $0^oC$ latent heat of fusion converts it to a form of ice. So, the given statement is true.

Multiple choice chemistry properties of natural resources conservation of water and recycling properties of water structure and properties of water

Ice at $0 \ ^0C$ has a lower density than water $4^{\circ}C$ and hence floats on water.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$H _{2} O$ at 4$ ^{\circ}C $ has maximum density. Ondecreasing the temperature from 4$ ^{\circ}C $ to 0$ ^{\circ}C $, its density decreases. Ice has 0$ ^{\circ}C $ has also less density compared to water at 4$ ^{\circ}C $. So, ice floats on water.