Tag: upthrust in fluids, archimedes' principle and floatation

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

If the density of a block is $981kg/{m^3}$ then it shall

physics upthrust in fluids, archimedes' principle and floatation applications of floatation principle of floatation and its applications when do objects float on water?

  1. Sink in water

  2. float with some part emmersed in water

  3. float completely immersed in watere

  4. float completely out of water.

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Correct Option: C

A cork of density $0.5\,gc{m^{ - 3}}$ floats on a calm swimming pool. The fraction of the cork's volume which is under water is:-

physics upthrust in fluids, archimedes' principle and floatation applications of floatation principle of floatation and its applications when do objects float on water?

  1. 0 %

  2. 25 %

  3. 10 %

  4. 50 %

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Correct Option: A

Consider a small balloon filled with an ideal gas which is submerged in water. Assuming that the temperature is the same everywhere in the water, the buoyant force on the balloon when it is at a depth d below the surface, in terms of its volume at the surface $V _ { 0 }$ , the atmospheric pressure $P _ { 0 }$ , the density of water $\rho _ { 0 }$ , and the acceleration due to gravity g.

physics upthrust in fluids, archimedes' principle and floatation applications of floatation principle of floatation and its applications when do objects float on water?

  1. $F _ { B } = \frac { P _ { 0 } V _ { 0 } } { d + \frac { P _ { 0 } } { \rho g } }$

  2. $F _ { B } = \frac { P _ { 0 } V _ { 0 } } { d \rho g + P _ { 0 } }$

  3. $F _ { B } = \frac { d \rho g + P _ { 0 } } { P _ { 0 } V _ { 0 } }$

  4. $F _ { B } = \frac { P _ { 0 } V _ { 0 } } { d + \frac { \rho g } { P _ { 0 } } }$

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Correct Option: C

A body is floating in water with $80$% of its volume below the surface of water. What is the density of body?

physics upthrust in fluids, archimedes' principle and floatation applications of floatation principle of floatation and its applications when do objects float on water?

  1. $666.7kg/{ m }^{ 3 }$

  2. $777.6kg/{ m }^{ 3 }$

  3. $800kg/{ m }^{ 3 }$

  4. $876.6kg/{ m }^{ 3 }$

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Correct Option: C

A body of mass $6kg$ immerses in water partially. If the body displaces $100$ g of water, then the apparent weight of the body is

physics upthrust in fluids, archimedes' principle and floatation applications of floatation principle of floatation and its applications when do objects float on water?

  1. $59$ N

  2. $40$ N

  3. $49$ N

  4. $60$ N

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Correct Option: A

A boat is floating in water at $0^{ \circ  }C$ such that 97% of the volume of the boat is submerged in water . The temperature at which the boat will just completely sink in water is $(\gamma _{ R }=3\times { 10 }^{ -4 }/{ ^{ 0 }C })(nearly)$ 

physics upthrust in fluids, archimedes' principle and floatation applications of floatation principle of floatation and its applications when do objects float on water?

  1. ${ 100 }{ ^{ 0 }C }$

  2. ${ 103 }{ ^{ 0 }C }$

  3. ${ 60 }{ ^{ 0 }C }$

  4. ${ 50 }{ ^{ 0 }C }$

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Correct Option: A

A dog weighing 5n kg is standing on a flat boat so that it is 10m from the shore . The dog walks 4 m on the boat towards the shore and then halts. The boat weighs 20kg and one can assume that there is no friction between it and the water .How far is the dog from the shore at the end of this time ?

physics upthrust in fluids, archimedes' principle and floatation applications of floatation principle of floatation and its applications when do objects float on water?

  1. 3.2 m

  2. 0.8 m

  3. 10 m

  4. 6.8 m

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Correct Option: D

An iceberg of density $900 kg/m3$ is floating in water of density $1000 kg/m3$. the percentage of volume of ice-cube outside the water is

physics upthrust in fluids, archimedes' principle and floatation applications of floatation principle of floatation and its applications when do objects float on water?

  1. $10$ percent

  2. $20$ percent

  3. $31$ percent

  4. none of the above

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Correct Option: A
Explanation:
Let  V is the total volume of iceberg
       ${ V } _{ sub }$ = volume of iceberg submerged
        ${ \rho  } _{ b }$= density of iceberg = 900 Kg/m3
         ${ \rho  } _{ w }$= density of water = 1000 Kg/m3
 So, for the flotation of body,
             weight of body= weight of water displaced
           $\Rightarrow{ \rho  } _{ b }V={ \rho  } _{ w }{ V } _{ sub }$
           $\Rightarrow \dfrac { { V } _{ sub } }{ V } =\dfrac { { \rho  } _{ b } }{ { \rho  } _{ w } } $
substracting both side from 1, we get
             $\Rightarrow 1-\dfrac { { V } _{ sub } }{ V } =1-\dfrac { { \rho  } _{ b } }{ { \rho  } _{ w } } $
            $\Rightarrow \dfrac { V-{ V } _{ sub } }{ V } =\dfrac { { \rho  } _{ w }-{ \rho  } _{ b } }{ { \rho  } _{ w } } $
             Converting it in percentage,
              $\Rightarrow \dfrac { V-{ V } _{ sub } }{ V } \times 100=\dfrac { { \rho  } _{ w }-{ \rho  } _{ b } }{ { \rho  } _{ w } } \times 100$
by  substituting values, we get
            percentage volume outside the water= $\dfrac { 1000-900 }{ 1000 } \times 100=10$%

A wooden cylinder floats vertically in water with half of its length immersed, Density of wood is

physics upthrust in fluids, archimedes' principle and floatation applications of floatation principle of floatation and its applications when do objects float on water?

  1. Equal to that of water

  2. Half the density of water

  3. Double the density of water

  4. One fourth the density of water

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Correct Option: C

A wooden cube floats in water partially immersed. When 200 g weight is put on the cube, it further immersed by 2 cm. The length of the side of the cube is

physics upthrust in fluids, archimedes' principle and floatation applications of floatation principle of floatation and its applications when do objects float on water?

  1. $1.0 cm$

  2. $\sqrt{10}cm$

  3. $10 cm$

  4. $20 cm$

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Correct Option: C