Tag: buoyancy

Questions Related to buoyancy

A cube of wood floats in water, with $42$% of its volume is submerged, then the density of the wood is

physics upthrust in fluids, archimedes' principle and floatation upthrust is equal to the weight of displaced liquid pressure in fluids buoyancy

  1. $42\ g\ cm^{-3}$

  2. $0.42\ g\ cm^{-3}$

  3. $0.58\ kg\ cm^{-3}$

  4. $600\ g\ cm^{-3}$

Show answer
Correct Option: B
Explanation:

By Archimedes Principle, the buoyant force on a body partially or fully immersed in a fluid is given by the weight of the fluid displaced.


Let the volume of wood be $V$
Thus, volume of wood submerged is $0.42V$

Thus, the buoyant force acting on the wood is $B = 0.42\rho gV$
Weight of wood is $\rho _\textrm{wood}gV$

Thus, in equilibrium, $0.42\rho gV = \rho _\textrm{wood}gV \Rightarrow \rho _\textrm{wood} = 0.42\rho$

As Density of water is $\rho = 1\textrm{ g cm}^{-3}$, we have $\rho _\textrm{wood} = 0.42 \textrm{ g cm}^{-3}$

A: Diver dives in and reaches a depth of 100m.
B: Diver swims up from the depth of 100m to the surface.
Choose the correct alternative:

physics upthrust in fluids, archimedes' principle and floatation upthrust is equal to the weight of displaced liquid pressure in fluids buoyancy

  1. A is easier than B

  2. B is easier than A

  3. A and B are equally hard

  4. A is easier than B if speed of descent and ascent is same and more.

Show answer
Correct Option: A
Explanation:
Assume:
$F _d: \text{Force applied by diver during descent in downward direction}$
$F _u: \text{Force applied by diver during ascent in upward direction}$
$U: \text{Upthrust}$
$m: \text{Mass of the diver}$
$g: \text{Acceleration due to gravity}$
Uniform ascent and descent.

Diver has more density than water. Hence, weight of diver is more than the upthrust and without any effort, the diver sinks.
i.e. $mg>U..................(1)$

During upward motion, $F _u+U-mg=0............(2)$
During downward motion, $F _d-U+mg=0...............(3)$

From (1),(2) and (3), 
$F _u-F _d=2mg-2U$
$F _u-F _d>0$
$F _u>F _d$

Mathematical proof of upthrust is based on 

physics upthrust in fluids, archimedes' principle and floatation upthrust is equal to the weight of displaced liquid pressure in fluids buoyancy

  1. Definition of pressure

  2. Weight of object

  3. Pressure exerted by a column of fluid

  4. Viscosity

Show answer
Correct Option: C
Explanation:
Mathematical proof:
Consider a cylinder of cross section area $A$ and height $L$ completely submerged in water. Let depth of upper surface be $h$.
Using, pressure exerted by fluid column:
Force on the upper face of the cylinder = $hρgA$
Force on the lower face of the cylinder = $[h + L]ρgA$
Difference in force = $LAρg$

But $LA$ is the volume of liquid displaced by the cylinder, and $LrgA$ is the weight of the liquid displaced by the cylinder.

Therefore there is a net upward force on the cylinder equal to the weight of the fluid displaced by it.

Buoyant force is directed

physics floatation buoyancy fluid pressure option b: engineering physics

  1. upwards

  2. downwards

  3. sideways

  4. at ll directions

Show answer
Correct Option: A
Explanation:

As evident from Archimedes' principle, buoyant force is the force applied upward on any object by a fluid.

When a solid is completely immersed in a fluid, the apparent loss of weight of solid is _______ volume of fluid displaced 

physics floatation buoyancy fluid pressure option b: engineering physics

  1. more than

  2. less than

  3. equal to

  4. cant say

Show answer
Correct Option: C
Explanation:

From the principle of Archimedes, loss of weight is equal to the weight of the liquid displaced.

When a body is fully immersed in a liquid the apparent loss in the weight of body is equal to :

physics floatation buoyancy fluid pressure option b: engineering physics

  1. volume of liquid displaced by the body

  2. density of the liquid

  3. weight of liquid displaced by the body

  4. none of these

Show answer
Correct Option: C
Explanation:

According to Archimedes principle, the weight of water displaced is equal to the weight of immersed part.For a solid floating in a liquid, its weight acting vertically down at its centre of gravity is equal to the weight of the liquid displaced by the immersed part of the solid acting vertically up at its centre of buoyancy. In the floating condition, the apparent weight and the apparent density of the solid are zero and the body is said to be weightless.

State whether the weight of an iron sinker with cork combined in water will be more or less than that of the iron sinker alone in water. 

physics floatation buoyancy fluid pressure option b: engineering physics

  1. Less

  2. More

  3. Same

  4. None of the above

Show answer
Correct Option: A
Explanation:

The weight of an iron sinker with cork combined in water will be less than that of the iron sinker alone in water.
This is because upthrust on cork due to water (when completely immersed) is greater than its weight.

An incompressible liquid of density $\rho$ is contained in a vessel of uniform cross-sectional area $A$. If then atmospheric pressure is $p$, then the force acting on a horizontal plane of area a situated at a depth $d$ in liquid is given by

physics option b: engineering physics buoyancy floatation fluid pressure

  1. $Ap+apgd$

  2. $\dfrac { p }{ A } +\dfrac { \rho gd }{ a }$

  3. $\dfrac { p+\rho gd }{ a }$

  4. $a\left( \rho\ gd+p \right)$

Show answer
Correct Option: D

A gas is enclosed in a rectangular vessel. $20 \times 10^23$ molecules of the gas strike a well of the vessel normally per second, with a velocity of 250m/s and rebound with the same speed in the opposite direction. What is the force exerted by the gas on the wall if the mass of each molecule is $5 \times 10^-23$ g ? 

physics option b: engineering physics buoyancy floatation fluid pressure

  1. 50 N

  2. 40 N

  3. 75 N

  4. 25 N

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Correct Option: A

A pump is required to lift 1000 kg of water per minute from a well 20 m deep and eject it at a rate of 20 $ms^-1$. What (horsepower engine is required for the purpose of lifting water)?

physics option b: engineering physics buoyancy floatation fluid pressure

  1. $4.46 HP$

  2. $4.36 HP$

  3. $3.96 HP$

  4. $8.85 HP$

Show answer
Correct Option: A