Tag: upthrust is equal to the weight of displaced liquid

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

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.

  1. $15/8$
  2. $1/8$
  3. $5/8$
  4. $15/2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The resultant downward thrust is calculated by integrating the pressure over the wetted surface area. For a cone with height h=2r, submerging half the axis means the liquid height is r. The calculation involves the weight of the displaced liquid and the pressure at the base, leading to the ratio 5/8.

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

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 

  1. $10\ cc$
  2. $90\ cc$
  3. $50\ cc$
  4. $9\ cc$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

According to the law of flotation, the weight of the floating object equals the weight of the displaced liquid. Therefore, Density_ice * Volume_ice = Density_water * Volume_submerged. Given 0.9 * 100 = 1 * Volume_submerged, the submerged volume is 90 cc.

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

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 $10^3 kg/m^3$)

  1. 6 cm

  2. 12 cm

  3. 8 cm

  4. 10 cm
Reveal answer Fill a bubble to check yourself
D Correct answer
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 $a=0.1\,m=10\,cm$
Multiple choice physics upthrust in fluids, archimedes' principle and floatation upthrust is equal to the weight of displaced liquid pressure in fluids buoyancy

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 

  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.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Buoyant force is equal to the weight of the displaced liquid, which is proportional to the volume of the object immersed. If the 3rd cube (V/8) experiences 40 units, the 2nd cube (V/4) has twice the volume, so it experiences 40 * 2 = 80 units.

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

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

  1. Rises

  2. Falls

  3. Unchanged

  4. First rises and then falls
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When the ice melts, the water level depends on the density of the object inside. Since the glass ball is denser than water, it displaces more water when it is part of the floating ice than it does when it sinks to the bottom after the ice melts, causing the level to fall.