Tag: pressure in fluids

Questions Related to pressure in fluids

A vessel in the shape of a hollow hemisphere surmounted by a cone is held with the axis vertical and vertex uppermost. If it be filled with a liquid so as to submerge half the axis of the cone in the liquid, and the height of the cone be double the radius of its base, find the value of $x$, where the resultant downward thrust of the liquid on the vessel is $x$ times the weight of the liquid that the hemisphere can hold.

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

  1. $15/8$

  2. $1/8$

  3. $5/8$

  4. $15/2$

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Correct Option: C

What is the area of the smallest block of ice $0.5\ m$ thick that will just support a man of mass $100\ kg$? The block of ice is floating in fresh water.$\left(SG\ of\ ice\ =0.9\right)$.

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

  1. $2m^{2}$

  2. $4m^{2}$

  3. $10m^{2}$

  4. $0.25m^{2}$

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Correct Option: B

A block of ice of density $0.9\ gm\ cc^{-1}$ and of volume $100\ cc$ floats in water. Then volume of ice inside the water 

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

  1. $10\ cc$

  2. $90\ cc$

  3. $50\ cc$

  4. $9\ cc$

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Correct Option: B

A wooden cube floating in water supports a mass m = 0.2 kg on its stop. When the mass is removed the cube rises by 2 cm. The side of the cube is - (density of water $10^3 kg/m^3$)

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

  1. 6 cm

  2. 12 cm

  3. 8 cm

  4. 10 cm

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Correct Option: D
Explanation:
Cube is floating, therefore
Weight of liquid displaced $=$ Weight of cube
let  the volume of liquid displaced $= V$
Density of liquid $= \rho$
Mass of cube $= M$

Then,

$(M+m)g=\rho v g$

$\implies M+m=\rho v$       ............(1)

When mass is removed, cube reise by $l=2\,cm$

Therefore,

$Mg=(V-lA)\rho g$

where, $AS$ is the are of face of cube

$\implies M=\rho(V-lA)$          .................(2)

Eliminating $M$ by subtracting (2) from (1)

$m=\rho l A$

$\implies A=\dfrac{m}{\rho l}$

Let side of cube $=a$

Then,

$a^2=A=\dfrac{m}{\rho l}$

$\implies a=\sqrt{\dfrac{m}{\rho l}}$

If liquid is water, then $\rho=1000\,kg/m^3$

$I=0.02\,m$ (given)

$m=0.2\,kg$ (given)

Putting these value, we get $a=0.1\,m=10\,cm$

Three cubes of volume $V , V / 4$ and $V / 8$ respectively are immersed in thesame liquid. If the buoyant force exerted on the $3 ^ { rd }$ cube is 40 units. Then 

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

  1. Buoyant force on $1 ^ { st }$ cube is 80 units.

  2. Buoyant force on $1 ^ { st }$ cube is 320 units.

  3. Buoyant force on $2 ^ { nd }$ cube is 80 units.

  4. Buoyant force on $2 ^ { nd }$ cube is 320 units.

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Correct Option: C

A body of mass  $40 kg$  floats on a lake with  $5 { cm }$  in water, when another block placed on the block,  $7 { cm }$  are submerged, the mass of second block is :

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

  1. $20{ kg }$

  2. $10{ kg }$

  3. $16{ kg }$

  4. $13{ kg }$

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Correct Option: A

A solid sphere weighs $40 N$ in water and $45 N$ in a liquid of relative density $0.7$5 when completely immersed. The weight of sphere in air will be 

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

  1. $50N$

  2. $53N$

  3. $80N$

  4. $60N$

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Correct Option: A

An ice block contains a glass ball when the ice melts within the water containing vessel, the level of water

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

  1. Rises

  2. Falls

  3. Unchanged

  4. First rises and then falls

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Correct Option: B

A body is floating in liquid with  $50\%$  of its volume out side the liquid. When the entire system accelerates upwards with an acceleration  $g / 3 ,$  the percentage of its volume outside the liquid is

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

  1. $33 \%$

  2. $50 \%$

  3. $25 \%$

  4. $66 \%$

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Correct Option: C

Ice pieces are floating in a beaker A containing water and also in a beaker B containing miscible liquid of specific gravity 1.2 When ice melts,the level of

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

  1. Water increases in A

  2. Water decreases in A

  3. Liquid in B decreases

  4. Liquid in B increases

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Correct Option: C