Tag: floating bodies

Questions Related to floating bodies

A dam of water reservoir is built thicker at bottom than at the top because

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

  1. pressure of water is very large at the bottom due to its large depth.

  2. water is likely to have more density at the bottom due to its large depth.

  3. quantity of the water at the bottom is very large.

  4. none of the above.

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Correct Option: A
Explanation:

The pressure applied to walls of the dam will be a function of the amount  of water that is over that particular point on the wall. So water pressure is very large at the bottom due to its large depth. That's why dams are constructed thicker at their bottoms than at their tops. So correct option is 'A'.

The height to which a cylindrical vessel be filled with a homogeneous liquid, to make the average force with which the liquid presses the side of the vessel equal to the force exerted by the liquid on the bottom of the vessel, is equal to

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

  1. half of the radius of the vessel

  2. one-fourth of the radius of the vessel

  3. three-fourth of the radius of the vessel

  4. three eight of the radius of the vessel

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Correct Option: A

A tank with a small hole at the bottom has been filled with water and kerosene (specific gravity 0.8). The height of water is 3m and that of kerosene 2m. When the hole is spend the velocity of fluid coming out from it is nearly .(take g=$10ms^{ -2 }$ and density of water = $10^{ 3 }kgm^{ -3 }$)

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

  1. ${ 10.7 }{ ms }^{ -1 }$

  2. ${ 9.8 }{ ms }^{ -1 }$

  3. ${ 8.5 }{ ms }^{ -1 }$

  4. ${ 7.6 }{ ms }^{ -1 }$

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Correct Option: C

A cylindrical tank having cross-sectional area $A$ is filled with water to a height of $2.0m$. A circular hole of cross-sectional area $a$ is opened at a heigh of $75cm$ from the bottom. If $\cfrac{a}{A}=\sqrt{0.2}$, the velocity with which water emerges from the ole is ($g=9.8m{s}^{-2}$)

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

  1. $4.9m{s}^{-1}$

  2. $4.95m{s}^{-1}$

  3. $5.0m{s}^{-1}$

  4. $5.5m{s}^{-1}$

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Correct Option: C

To what height $h$ should a cylindrical vessel of diameter $d$ be filled with a liquid so that due to liquid force on the vertical surface of the vessel be equal to the force on the bottom:

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

  1. $h=d$

  2. $h=2d$

  3. $h=3d$

  4. $h=d/2$

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Correct Option: A

If pressure at half the depth of a lake is equal to $2/3$ pressure at the bottom of the lake then what is 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. 10m

  2. 20m

  3. 30m

  4. 60m

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Correct Option: B

Water flows into a large tank with flat bottom at the rate of $ 10^{-4} m63s^{-1} $. water is also leaking out of a hole of area $ 1cm^2 $ at its bottom. if the height of the water in the tank remains steady , then this height is: 

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

  1. 5.1 cm

  2. 1.7 cm

  3. 4 cm

  4. 2.9 cm

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Correct Option: A

If the system is not in free fall, which of the following statements are true about hydrostatic pressure?

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

  1. In a liquid, point at different depths can never be at the same pressure.

  2. In a liquid, points at different depths may be at the same pressure.

  3. In different liquids, points at different depths can be at the same pressure.

  4. In different liquids, points at the same depth can never be at same pressure.

Show answer
Correct Option: A,C,D
Explanation:

Pressure difference = $density\times a\times difference ~in ~depths$
(a)In a given liquid density remains same.So, pressure is same only at points of equal depth.
(c)In different liquids,pressure can be same at different depths if ${\rho}^{} _{1} {h}^{} _{1}$ = ${\rho}^{} _{2} {h}^{} _{2}$
 (d)${\rho}^{} _{1} \neq {\rho}^{} _{2}$ & ${h}^{} _{1} = {h}^{} _{2}$ implies ${P}^{} _{1} \neq {P}^{} _{2}$

How is the reading of a barometer affected when it is taken to (i) a mine, and (ii) a hill?

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

  1. (i) increases, (ii) decreases.

  2. (i) decreases, (ii) increases.

  3. (i)remains same (ii) decreases

  4. (i) increases, (ii) remains same

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Correct Option: A
Explanation:

(i) increases due to increase in height of atmosphere above it.
(ii) decreases. due to decrease in height of atmosphere above it.

The volume of an air bubble becomes three times as it rises from the bottom of a take to its surface. Assuming atmospheric pressure to be $75\ cm$ of $Hg$ and the density of water to be $\displaystyle \dfrac{1}{10}$ of the density of mercury, the depth of the take is :

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

  1. $5\ m$

  2. $10\ m$

  3. $15\ m$

  4. $20\ m$

Show answer
Correct Option: C
Explanation:

Since, the temperature of the surroundings remains constant, we can safely assume that the process is isothermal.

Therefore, applying Boyle's Law
$ P _1 V _1 = P _2 V _2 $

Let 1 denote the surface of water and 2 denote the depth

$ P _1 = 75 cm Hg $

$ P _2 = 75 + h/10 $ where h is the depth of the lake

$ V _1 = 3 V _2 $

Substituting the values, 

$ 75 \times 3 = 75 + \frac {h}{10} $

Solving, h = 1500 cm or 15 m