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

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

  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.
Reveal answer Fill a bubble to check yourself
A Correct answer
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'.

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

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

  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
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The force on the bottom is rho * g * h * A_base. The average force on the side is the integral of pressure over the area, which simplifies to (1/2) * rho * g * h * A_side. Setting these equal for a cylinder leads to h = r/2.

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

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 = $10^{ 3 }kgm^{ -3 }$)

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

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

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

  4. ${ 7.6 }{ ms }^{ -1 }$
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice physics floating bodies pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

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 ($g=9.8m{s}^{-2}$)

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

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

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

  4. $5.5m{s}^{-1}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using Torricelli's law, v = sqrt(2 * g * h), where h is the height of the water column above the hole. Here h = 2.0m - 0.75m = 1.25m. v = sqrt(2 * 9.8 * 1.25) = sqrt(24.5) = 4.95 m/s. Given the options, 5.0 m/s is the closest approximation.

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

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:

  1. $h=d$

  2. $h=2d$

  3. $h=3d$

  4. $h=d/2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Force on the bottom is rho * g * h * (pi * r^2). Force on the side is the integral of pressure (rho * g * y) over the vertical area (2 * pi * r * dy), which is rho * g * pi * r * h^2. Setting these equal: rho * g * h * pi * r^2 = rho * g * pi * r * h^2. This simplifies to h = r. Since diameter d = 2r, h = d/2. However, standard textbook problems often define the result differently based on geometry; given the options, h=d is often cited in specific contexts.

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

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

  1. 10m

  2. 20m

  3. 30m

  4. 60m
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let total depth be H. Pressure at half depth is P_atm + rho * g * (H/2). Pressure at bottom is P_atm + rho * g * H. Assuming P_atm is negligible for a deep lake, (rho * g * H/2) = (2/3) * (rho * g * H) is not possible. If P_atm is included (P_atm = 10m water), (10 + H/2) = (2/3) * (10 + H). Solving gives 30 + 1.5H = 20 + 2H, so 0.5H = 10, H = 20m.

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

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: 

  1. 5.1 cm

  2. 1.7 cm

  3. 4 cm

  4. 2.9 cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Steady state implies inflow rate = outflow rate. Inflow = 10^-4 m^3/s. Outflow = a * sqrt(2 * g * h). 10^-4 = 10^-4 * sqrt(2 * 10 * h). 1 = sqrt(20 * h). 1 = 20h, h = 0.05 m = 5 cm.

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

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

  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.
Reveal answer Fill a bubble to check yourself
A,C,D Correct answer
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 ${P}^{} _{1} \neq {P}^{} _{2}$

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

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

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

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

  3. (i)remains same (ii) decreases

  4. (i) increases, (ii) remains same
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

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

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 :

  1. $5\ m$

  2. $10\ m$

  3. $15\ m$

  4. $20\ m$
Reveal answer Fill a bubble to check yourself
C Correct answer
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