Tag: experimental verification of archimedes' principle

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

An object is placed in 3 beakers containing liquids A, B and C respectively. If the density of object (d) when compared to tensities of liquids A, B and C is given by $d _A < d < d _B < d _C$ then the body sinks in

  1. liquid A

  2. liquid B

  3. liquid C

  4. all the three liquids
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

When the density of the liquid is greater than that of object, then the weight of liquid displaced is greater than or equal to the weight of the object. This means that the buoyant force acting on the object is greater or equal to the weight of the object which makes the object to float in that liquid. 

Hence the object will float in liquids B and C as the densities of liquids B and C are more than that of the object while the object will sink in liquid A as the density of liquid A is less than that of the object.

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

A body of mass $120kg$ and density $600kg/{m}^{3}$ floats in water. What additional mass could be added to the body so that the body will just sink?

  1. $20kg$
  2. $80kg$
  3. $100kg$
  4. $120kg$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Weight of the water displaced= weight of body + additional mass

${ \rho  } _{ w }Vg=Mg$   ($M$ is the total mass)
${ \rho  } _{ w }V=M=\left( 100+m \right) \ V=\cfrac { 120 }{ 600 } =0.2{ m }^{ 3 }\ 1000\times 0.2=\left( 120+m \right) \ m=80kg$

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

Write the following steps in a sequence to verify Archimedes' principle.
(a) The object is completed immersed in a liquid.
(b) The weight of the object in air is measured by using a spring balance ($w _{1}$).
(c) The weight of the object in the given liquid is determined ($w _{1}$).
(d) The loss of weight of the object ($w _{1}-w _{2}$) is determined.
(e) The weight of the liquid displaced by the object (w) is determined.
(f) The value of ($w _{1}-w _{2}$) is compared with the value of (w).

  1. b a c d e f

  2. a b d c f e

  3. a b c d e f

  4. f e c a b d
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Option (A) follows correct procedure as initially weight of the object is calculated in the air than it is immersed in liquid and its weight is measured in the liquid and then the diffrence between the two weights would be calculated  and than weight of liquid displaced by the body would be calculated and later the two diffrences would e compared.

so option (A) is correct.

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

A body of density $\rho$ is dropped from rest from a height h into a lake of density $\sigma$, where $\sigma > \rho$. Neglecting all dissipative forces, the maximum depth to which the body sinks before returning to float on surface

  1. $\dfrac{h}{\sigma - \rho}$
  2. $\dfrac{h\rho}{\sigma}$
  3. $\dfrac{h\rho}{\sigma - \rho}$
  4. $\dfrac{h\sigma}{\sigma - \rho}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

${V _f}^2-V _1^2=2as$

$\Rightarrow r-(2gh)=2 \times -\left(\cfrac {\sigma}{\delta}-1\right)g \times s$
$\Rightarrow s=\left(\cfrac {h}{\cfrac {\sigma}{\delta}-1}\right)$
$\Rightarrow \left[s=\cfrac {h\rho}{\sigma-\rho}\right]$

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

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  $\rho _{wood} < \rho _{water}$)

  1. Sphere of iron will sink.

  2. Sphere of wood will sink.

  3. both will sink

  4. both will not sink
Reveal answer Fill a bubble to check yourself
A Correct answer
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. 

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

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 $\rho _L$?

  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 $\rho _s < \rho _L$.
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

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

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$=1020\ kg/m^3)$?

  1. $1350\ kg$
  2. $7830\ kg$
  3. $9200\ kg$
  4. $19,500\ kg$
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $7830 kg.$
Multiple choice physics upthrust in fluids, archimedes' principle and floatation experimental verification of archimedes' principle archimedes' principle archimedes' principle and its applications

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 ${ \sigma  } _{ 2 }$.

  1. $50\%$ submerged
  2. $25\%$ submerged
  3. $75\%$ submerged

  4. Fully submerged
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using the equilibrium condition for floating bodies and the given ratios, the forces balance such that the upper block is fully supported by the buoyancy of the lower block and its own displacement.