Tag: upthrust in fluids, archimedes' principle and floatation

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

$A$ and $B$ are two metallic pieces. They are fully immersed in water and then weighed. Now they show same loss of weight. The conclusion therefore is:

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

  1. $A$ and $B$ have same weight in air

  2. $A$ and $B$ have equal volumes

  3. The densities of the materials of $A$ and $B$ are the same

  4. $A$ and $B$ are immersed to the same depth inside water.

Show answer
Correct Option: B
Explanation:

Same loss of weight implies equal buoyant forces on the object which is equal to weight of liquid displaced i.e. both the bodies have equal volumes.

Two solids A and B Float is a liquid. It is observed that A floats with half its volume immersed and B floats with $2/3$ of its volume immersed. Compare the densities of A and B.

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

  1. $4:3$

  2. $2:3$

  3. $3:4$

  4. $1:3$

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Correct Option: C
Explanation:

$\dfrac { density\quad of\quad A }{ density\quad of\quad B } =\dfrac { density\quad of\quad immersed }{ Volume\quad of\quad B\quad immersed } =\dfrac { 1/2 }{ 2/3 } $

$\dfrac { density\quad of\quad A }{ density\quad of\quad B } =\dfrac { 3 }{ 4 } $

A piece of paraffin wax of density 0.9 g/cc floats on water.A layer of turpentine of density 0.87 g/cc is added on top of water until the wax is entirely submerged.The ratio of the volume of wax immersed in water to that in turpentine is 

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

  1. 3 : 13

  2. 87 : 90

  3. 90 : 87

  4. 3 : 10

Show answer
Correct Option: D
Explanation:

Buoyant force = weight of liquid displaced

hence $0.9V=1\times { V } _{ 1 }+0.87\times { V } _{ 2 }$
            & $V={ V } _{ 1 }+{ V } _{ 2 }$
               $0.9\left( { V } _{ 1 }+{ V } _{ 2 } \right) ={ V } _{ 1 }+0.87{ V } _{ 2 }$
               $0.9{ V } _{ 1 }+0.9{ V } _{ 2 }={ V } _{ 1 }+0.87{ V } _{ 2 }$
                        $\boxed { \dfrac { { V } _{ 1 } }{ { V } _{ 2 } } =\dfrac { 3 }{ 10 }  } $

A 70 g substance has a volume of $35:cm^3$. It will float on the surface of the water.

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

  1. True

  2. False

Show answer
Correct Option: B
Explanation:

Given:
Mass of substance $= 70g$.
Volume of substance $= 35cm^3$
density of water $= 1gm^{-3}$
By using the formula,
Density $=\dfrac{Mass}{Volume}$
Density of sub stance $= \dfrac{70}{35}=2gm^{-3}$
since, the density of the substance is more than the density, the gravitational force acting on it will be stronger than the buoyant force of water acting it, it will sink and not float on the surface of water

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

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

  1. liquid A

  2. liquid B

  3. liquid C

  4. all the three liquids

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Correct Option: A
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.

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?

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

  1. $20kg$

  2. $80kg$

  3. $100kg$

  4. $120kg$

Show answer
Correct Option: B
Explanation:

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

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

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).

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

  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

Show answer
Correct Option: A
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.

The density of ice is $917\ kgm^{-3}$. What fraction of the volume of a piece of ice will be above water, when floating in fresh water?

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

  1. 0.06

  2. 0.083

  3. 0.038

  4. 0.068

Show answer
Correct Option: C

Construction of a submarine is based on.

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

  1. Bernoulli's theorem

  2. Pascal's law

  3. Archimedes' principle

  4. None of these

Show answer
Correct Option: C
Explanation:

Construction of a submarine is based on Archimedes' principle.

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

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

  1. $\dfrac{h}{\sigma - \rho}$

  2. $\dfrac{h\rho}{\sigma}$

  3. $\dfrac{h\rho}{\sigma - \rho}$

  4. $\dfrac{h\sigma}{\sigma - \rho}$

Show answer
Correct Option: C
Explanation:

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

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