GATE Overflow for GATE XE - Recent activity in Hydrostatics

Edited: GATE XE 2026 | Question: 149

Thu, 02 Apr 2026 10:22:55 +0000

In a stable atmosphere, the change in pressure (in kilo Pascal) at a height of $100 \mathrm{~m}$ from the mean sea level is $\_\_\_\_$. (rounded off to three decimal places)

[Density of air is $1.029 \mathrm{~kg} \mathrm{~m}^{-3}$ and acceleration due to gravity is $9.81 \mathrm{~m} \mathrm{~s}^{-2}$]

Edited: GATE XE 2026 | Question: 30

Tue, 31 Mar 2026 07:57:08 +0000

A rectangular block (density $=600 \mathrm{~kg} \cdot \mathrm{~m}^{-3}$ ) with base area of $0.06 \mathrm{~m}^{2}$ and height $15$ cm is partially submerged in water (density $=1000 \mathrm{~kg} \cdot \mathrm{~m}^{-3}$), as shown in the figure. Assume acceleration due to gravity as $10 \mathrm{~m}. \mathrm{s}^{-2}$. The submerged depth, $h$ (in $\mathrm{m}$) of the block in the water is $\_\_\_\_$. (rounded off to two decimal places)

Edited: GATE XE 2025 | Question: 172

Mon, 30 Jun 2025 16:28:12 +0000

A floating hot air balloon with volume $1000 \mathrm{~m}^{3}$ and gross mass (excluding the air in the balloon) $100 \: \mathrm{kg}$ is in hydrostatic balance where the external air temperature is $10^{\circ} \mathrm{C}$ and density is $1 \mathrm{~kg} \mathrm{~m}^{-3}$. The temperature of the air inside the balloon is $\_\_\_\_\_\_$ ${ }^{\circ} \mathrm{C}$. (Round off to the nearest integer.)

Edited: GATE XE 2025 | Question: 33

Sun, 29 Jun 2025 12:44:37 +0000

A solid body of uniform specific gravity floats in a deep liquid pool. Take $B, G$, and $M$ as the centre of buoyancy, centre of gravity, and metacentre of the body, respectively.

Which one of the following options is correct for the stable floatation of the body in the pool when the body is given a small tilt angle?

$\overline{M G}$ is the metacentric height and $G$ should lie below $M$
$\overline{M G}$ is the metacentric height and $B$ should lie above $M$
$\overline{M B}$ is the metacentric height and $B$ should lie below $M$
$\overline{M B}$ is the metacentric height and $G$ should lie above $M$

Recategorized: GATE XE 2024 | Question: 19

Mon, 05 May 2025 14:40:48 +0000

For an immersed neutrally buoyant body to be in stable equilibrium, the center of gravity of the body is directly

above the metacenter.
below the metacenter.
above the center of buoyancy.
below the center of buoyancy.

Recategorized: GATE XE 2024 | Question: 25

Mon, 05 May 2025 14:40:28 +0000

A vessel which contains a volatile liquid and its vapour is connected with a mercury manometer as shown in figure. Both the liquid and vapour phases are at equilibrium. The vapour pressure and density of the volatile liquid are $107.6$ kPa and $700 \mathrm{~kg} / \mathrm{m}^{3}$, respectively. The density of the mercury is $13600 \mathrm{~kg} / \mathrm{m}^{3}$. Acceleration due to gravity $(\mathrm{g})$ is $10 \mathrm{~m} / \mathrm{s}^{2}$ and atmospheric pressure is $101$ kPa . Hydrostatic pressure created by the weight of the vapour is neglected.

The height, $h$ $\text{(in m , rounded off to two decimal places)}$ of the mercury column in figure is ____________.

Recategorized: GATE XE 2022 | Question: 12

Mon, 05 May 2025 12:43:57 +0000

A heavy horizontal cylinder of diameter $D$ supports a mass of liquid having density $\rho$ as shown in the figure. Find out the vertical component of force exerted by the liquid per unit length of the cylinder if $g$ is the acceleration due to gravity.

$\frac{\pi D^{2}}{4} \rho g$
$\frac{\pi D^{2}}{8} \rho g$
$\frac{\pi D^{2}}{2} \rho g$
$\frac{\pi D^{2}}{3} \rho g$

Recategorized: GATE XE 2022 | Question: 31

Mon, 05 May 2025 12:43:01 +0000

A wooden cylinder $\text{(specific gravity}$ $=0.6$ ) of length $L$ and diameter $D$ floats in water $\text{(density}$ $1000 \mathrm{~kg} / \mathrm{m}^3$). Find out the minimum value of $D / L$ for which the cylinder floats with its axis vertical.
$\text{(Round off to three decimal places)}$

Recategorized: GATE XE 2023 | Question: 20

Mon, 05 May 2025 12:21:25 +0000

A stationary object is fully submerged in a static fluid, as shown in the figure. Here, $\text{CG}$ and $\mathrm{CB}$ stand for center of gravity and center of buoyancy, respectively. Which one(s) among the following statements is/are true?

The object is in stable equilibrium if $y_{C G}>y_{C B}$.
The object is in stable equilibrium if $y_{C G}$
The object is in neutral equilibrium if $y_{C G}=y_{C B}$.
The object is in unstable equilibrium if $y_{C G}=y_{C B}$.

Recategorized: GATE XE 2023 | Question: 33

Mon, 05 May 2025 12:20:43 +0000

Q. 43 A stationary circular pipe of radius $R=0.5 \mathrm{~m}$ is half filled with water (density =
$1000 \mathrm{~kg} / \mathrm{m}^{3}$ ), whereas the upper half is filled with air at atmospheric pressure, as
shown in the figure. Acceleration due to gravity is $g=9.81 \mathrm{~m} / \mathrm{s}^{2}$. The magnitude
of the force per unit length (in $\mathrm{kN} / \mathrm{m}$, rounded off to one decimal place) applied by
water on the pipe section $\mathrm{AB}$ is

Recategorized: GATE XE 2023 | Question: 162

Mon, 05 May 2025 12:13:56 +0000

Q. 172
A cylindrical tank containing water is rotating about the z-axis at a constant angular velocity of $10 \mathrm{rad} \mathrm{s}^{-1}$. The schematic of the isobaric surface is shown in the following illustration, where ' $\mathrm{A}$ ' and ' $\mathrm{B}$ ' are two points on the isobaric surface at heights ' $z_{1}$ ' and ' $z_{2}$ ', respectively. Assuming the atmospheric pressure to be negligible and no transient flow, estimate the elevation difference in $\mathrm{m}$ between ' $\mathrm{z}_{1}$ ' and ' $\mathrm{z}_{2}$ '.
(consider $\mathrm{r}_{1}=0.5 \mathrm{~m}, \mathrm{r}_{2}=1.0 \mathrm{~m}$ and gravitational acceleration $g=9.8 \mathrm{~m} \mathrm{~s}^{-2}$, rounded off to two decimal places)