Tag: upthrust in fluids, archimedes' principle and floatation

Questions Related to upthrust in fluids, archimedes' principle and floatation

A sphere of iron and another of wood, both of same radius are placed on the surface of water. State which of the two will sink? (It is given $\rho _{iron} > \rho _{water}$, and  $\rho _{wood} < \rho _{water}$)

physics upthrust in fluids, archimedes' principle and floatation experimental verification of archimedes' principle archimedes' principle archimedes' principle and its applications

  1. Sphere of iron will sink.

  2. Sphere of wood will sink.

  3. both will sink

  4. both will not sink

Show answer
Correct Option: A
Explanation:

Since density of iron is more than that of wood, so weight of iron sphere will be more than upthrust due to water on it. But density of wood is less than that of iron so sphere of wood will float. 

How does the density of a substance determine whether a solid piece of density $\rho _s$ of that substance will float or sink in a given liquid of density $\rho _L$?

physics upthrust in fluids, archimedes' principle and floatation experimental verification of archimedes' principle archimedes' principle archimedes' principle and its applications

  1. The body will float if $\rho _s \leq \rho _L$ and it will sink if $\rho _s < \rho _L$.

  2. The body will float if $\rho _s \leq \rho _L$ and it will sink if $\rho _s > \rho _L$.

  3. The body will float if $\rho _s > \rho _L$ and it will sink if $\rho _s > \rho _L$.

  4. The body will float if $\rho _s > \rho _L$ and it will sink if $\rho _s < \rho _L$.

Show answer
Correct Option: B
Explanation:

The body will float if $\rho _{s}$ < $\rho _{L}$ and it will sink if $\rho _{s}$ > $\rho _{L}$
If the density of the substance is less than the density of the liquid, then the substance will float in liquid.
If the density of the substance is greater than the density of the liquid, then the substance will sink in liquid.

The dimensions of a wooden raft (density $ =150\ kg/ m^3)$ are $3.0\ m\times 3.0\ m\times 1.0\ m$. What maximum load can it carry in seawater so that the plank just floats in water (density$=1020\ kg/m^3)$?

physics upthrust in fluids, archimedes' principle and floatation experimental verification of archimedes' principle archimedes' principle archimedes' principle and its applications

  1. $1350\ kg$

  2. $7830\ kg$

  3. $9200\ kg$

  4. $19,500\ kg$

Show answer
Correct Option: B
Explanation:
Buoyancy is the upward force that an object feels from the water and when compared to the weight of the object.

Buoyancy force can be calculated with the equation 
$Fb=Vs\times D\times g$

where $F _b$ is the buoyancy force, $V _s$ is the submerged volume, $D$ is the density of the fluid the object is submerged in, and $g$ is the force of gravity.

It can also be given as the sum of the weight of the raft and the weight of the load. That is, ${ W } _{ raft }+{ W } _{ load }$ = $Fb=Vs\times D\times g$.

The weight of the raft
${ W } _{ raft }={ V } _{ raft }{ D } _{ raft }g$.

At maximum load, Volume of water displaced is equal to volume of the raft.

${ max(W } _{ load })=({ D } _{ water }-{ D } _{ raft }){ V } _{ raft }g$.
=$(1020kg/{ m }^{ 3 }-150kg/{ m }^{ 3 })(3m\times 3m\times 1m)g$
$=7830 kg.$

Hence, the maximum load the raft can carry sea water so that the plank just floats in water is $7830 kg.$

Two unequal blocks place over each other of different densities ${ \sigma  } _{ 1 }$ and ${ \sigma  } _{ 2 }$ are immersed in fluid of density of $\sigma$. The block of density ${ \sigma  } _{ 1 }$ is fully submerged and the block of density ${ \sigma  } _{ 2 }$ is partly submerged so that ratio of there masses is $1/2$ and $\sigma/{ \sigma  } _{ 1 }=2$ and $\sigma/{ \sigma  } _{ 2 }=0.5$. Find the degree of submergence of the upper block of density ${ \sigma  } _{ 2 }$.

physics upthrust in fluids, archimedes' principle and floatation experimental verification of archimedes' principle archimedes' principle archimedes' principle and its applications

  1. $50\%$ submerged

  2. $25\%$ submerged

  3. $75\%$ submerged

  4. Fully submerged

Show answer
Correct Option: D

A bob's weight is measured by a spring balance. Its volume is $10 cm^3$. In vacuum it measures $80 g$. What does it weigh in water?

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

  1. $70 g$

  2. $80 g$

  3. $90 g$

  4. $76 g$

Show answer
Correct Option: A
Explanation:

Weight of bob $= 80g/1000 N$ where $g$ is acceleration due to gravity

Weight of water displaced $= 10\times1\times g/1000 = 10g/1000 N$
Apparent weight$ = 80g/1000 - 10g/1000 = 70g/1000 N$
Weight measured $= 70/1000kg = 70 g$

Upthrust due to fluid equals

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

  1. Volume of liquid displaced

  2. Mass of liquid displaced

  3. Weight of liquid displaced

  4. None of the above

Show answer
Correct Option: C
Explanation:

Upthrust equals weight of fluid displaced by the object.

A ship has volume of $1,50,000 m^3$. It submerges $10\%$ in water. Upthrust felt by it equals

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

  1. $15 \times 10^6 N$

  2. $15 \times 10^7 N$

  3. $15 \times 10^8 N$

  4. $15 \times 10^5 N$

Show answer
Correct Option: B
Explanation:

Volume submerged$ = 15,000 m^3 $

Upthrust $= 15000m^3 \times 1000 kg/m^3 \times 10 m/s^2$
$=15 \times 10^7 N$

Consider a cylinder of height $h$ and Cross sectional area $A$ completely submerged in a fluid of density $\rho$. What is upthrust?

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

  1. $Ah\rho g$

  2. $Ah\rho /g$

  3. $A\rho g$

  4. $Ah^2 \rho g$

Show answer
Correct Option: A
Explanation:

Upthrust = weight of fluid displaced

= Vol of fluid displaced x density of fluid x acc. due to gravity
$=Ah\rho g$

An object having relative density 0.56 is dropped in water. Will it float or sink in water?

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

  1. Sink

  2. Float

  3. Depends on the density of water

  4. Unsure

Show answer
Correct Option: B
Explanation:

Explanation: the relative density of water is 1 and that of the object is less than 1. Thus the upthrust experienced by the object will be more than the weight of the object making it float on the surface of water.

A body of density equal to density of fluid is sinking at speed of $1 m/s$ at $t=0$. What is distance covered by object in $1s$? 

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

  1. $0.5m$

  2. $1m$

  3. $0.75m$

  4. $0.875m$

Show answer
Correct Option: B
Explanation:

Upthrust = weight of the body since density of body equals density of fluid

Hence, Net force $= 0$ and acceleration$ = 0$
Distance = speed x time$ = 1m$