Tag: floating bodies

Questions Related to floating bodies

 The average pressure of a liquid (density$\rho$) on the walls of the container filled upto height $h$ with the liquid is $\dfrac{1}{2}h\rho g$.

physics floating bodies pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

  1. True

  2. False

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Correct Option: A

A spherical bubble of air has a radius of $1$mm at the bottom of a tank full of water. As the bubble rises it goes on becoming bigger on reaching the surface, the radius becomes $2$mm. The depth of tank is

physics floating bodies pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

  1. $142.80$m

  2. $72.35$m

  3. $723$m

  4. $100$m

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Correct Option: B

The pressure at point in water is $10\ N/m^{2}$. The depth blow this point where the pressure becomes double is (Given density of water $=10^{3}\ kh\ m^{-3},\ g=10\ m\ s^{-2}$)

physics floating bodies pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

  1. $1\ mm$

  2. $1\ cm$

  3. $1\ m$

  4. $10\ cm$

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Correct Option: D

Two vessels A and B are different shapes have the same base area and are filled with water upto same height as the force exerted between water on the base is FA for vessel A and F B for vessel B . The respective weight of the water filled in vessel are wA and wB. Then

physics floating bodies pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

  1. FA>FB , was>wB

  2. FA=FB, wA>wB

  3. FA=FB, wA

  4. FA>FB, wA=wB

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Correct Option: A

The reading of a barometer containing some air above the mercury column is $73\ cm$ while that of a correct one is $76\ cm$. If the tube of the faulty barometer is pushed down into mercury until volume of air in it is reduced to half, the reading shown by it will be

physics floating bodies pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

  1. $70\ cm$

  2. $72\ cm$

  3. $74\ cm$

  4. $76\ cm$

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Correct Option: A

A large container of negligeble mass and uniform cross-section area A has a small hole (of area a < < A) near its side wall at bottom. The container is open at the top and kept on a smooth horizontal floor . It contains a liquid of density $\rho $ and mass $m _0$ when liquid starts flowing horizontally at time t = 0. Find the speed of container when 75% of the liquid has drained out (Assume the liquid surface remains horizontal throughout the motion)

physics floating bodies pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

  1. $\left[ \frac { { m } _{ 0 }g }{ A\rho } \right] ^{ 1/2 }$

  2. $\left[ \frac { { 4m } _{ 0 }g }{ A\rho } \right] ^{ 1/2 }$

  3. $\left[ \frac { { m } _{ 0 }g }{ 2A\rho } \right] ^{ 1/2 }$

  4. $\left[ \frac { { 2m } _{ 0 }g }{ A\rho } \right] ^{ 1/2 }$

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Correct Option: C

A large vessel with a small hole at the bottom is filled with water and kerosene. The height of the water column is 20 cm and that of the kerosene is 25 cm. the velocity with which water flows out the hole is

physics floating bodies pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

  1. 2 m/s

  2. 4 m/s

  3. 2.8 m/s

  4. 1 m/s

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Correct Option: C

A large cylinderical vessel contains water to a height of $10m$ it is found taht the acting on the curved surface is equal to that at the bottom. If atmospheric pressure can supposed a semi column of $10m$, the radius of the vessel is

physics floating bodies pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

  1. $10m$

  2. $15m$

  3. $5m$

  4. $25m$

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Correct Option: B

If the atmospheric pressure is 76 cm of Hg at what depth of water in a lake the pressure will becomes 2 atmospheres nearly.

physics floating bodies pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

  1. $862 cm$

  2. $932 cm$

  3. $982 cm$

  4. $1033 cm$

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Correct Option: D
Explanation:

Pressure at that depth $= 2$ atmosphere $= 2 \times 76\, cm$ of $Hg$

Pressure is due to atmosphere $+$ pressure due to column of 
water $= 2 \times  76\, cm$ of $Hg$ 
$\implies 76\, cm$ of $Hg +$ depth $\times$ density of 
water $\times g = 2 \times  76 cm$ of $Hg$
Or 

$h \times d \times g = 76\, cm$ of $Hg$
Or 

$h = 76 \,cm \times  13600 \times \dfrac{g }{ 1000} \times g$  

Note: pressure due to $h$ meter of $Hg =h\times density\,of\,mercury \times g$$ 

Cancelling $g$ we have 

$h = 13.6 \times 76 = 1033.6 \,cm $ ( as cm is taken for atmosphere answer too comes in cm)

The pressure at the bottom of a lake, due to water is $4.9 \times 10 ^ { 6 } \mathrm { N } / \mathrm { m } ^ { 2 }$ . Whatis the depth of the lake? 

physics floating bodies pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

  1. 500$\mathrm { m }$

  2. 400$\mathrm { m }$

  3. 300$\mathrm { m }$

  4. 200$\mathrm { m }$

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Correct Option: A