Accelerating Containers

Q. Angle of inclination of the water surface from horizontal for the given accelerated container shown in the figure is [Assume $g=10{\text{m/s}}^2$]

1. ${45}^{\circ }$
2. ${30}^{\circ }$
3. ${60}^{\circ }$
4. ${70}^{\circ }$

Q. A vessel containing water has a constant acceleration of $19.6{\text{m/s}}^2$ along horizontal direction. The free surface of water will be inclined with the horizontal at an angle of : [Take $g=9.8{\text{m/s}}^2$]

1. ${\tan }^{-1}\left[\frac{1}{2}\right]$
2. ${\sin }^{-1}\left[\frac{1}{\sqrt{3}}\right]$
3. ${\tan }^{-1}\left[\sqrt{2}\right]$
4. ${\sin }^{-1}\left[\frac{2}{\sqrt{5}}\right]$

Q. The closed container shown in the figure is filled with water and accelerating. Then, minimum and maximum pressure is at -

1. $A$ and $B$ respectively
2. $B$ and $C$ respectively
3. $B$ and $D$ respectively
4. $D$ and $A$ respectively

Q. A closed tube filled with water is rotating about an axis as shown in figure. The pressure difference $P_A-P_C$ is

1. $-12\times {10}^3{\text{N/m}}^2$
2. $-24\times {10}^3{\text{N/m}}^2$
3. $6\times {10}^3{\text{N/m}}^2$
4. $20\times {10}^3{\text{N/m}}^2$

Q. Liquid is kept in a container having square cross section. It is now accelerated from left to right with an acceleration of $5{\text{m/s}}^2$. Due to this the free surface makes some inclination with horizontal. If the length of the square cross section is $10\text{m}$, find the difference in heights of liquid at the left and the right wall. (Take $g=10{\text{m/s}}^2$)

1. $4\text{m}$
2. $5\text{m}$
3. $6\text{m}$
4. $10\text{m}$

Q. A closed rectangular tank is completely filled with water and is accelerated horizontally with an acceleration $a$ towards right as shown in figure. Then pressure is maximum and minimum (respectively) at:

1. $B$ and $D$
2. $C$ and $D$
3. $B$ and $C$
4. $B$ and $A$

Q. When a half filled water tanker accelerates, the pressure on the back wheel increases.

1. True
2. False

Q. Consider an elevator accelerating vertically upwards and a car accelerating on a horizontal road. The pressure in a liquid at two points on the same horizontal plane are equal in which of the situations?

1. The car only
2. The elevator only
3. Both of them
4. None of them

Q. A vessel containing water has a constant acceleration of $19.6{\text{m/s}}^2$ along horizontal direction. The free surface of water will be inclined with the horizontal at an angle of : [Take $g=9.8{\text{m/s}}^2$]

1. ${\tan }^{-1}\left[\frac{1}{2}\right]$
2. ${\sin }^{-1}\left[\frac{1}{\sqrt{3}}\right]$
3. ${\tan }^{-1}\left[\sqrt{2}\right]$
4. ${\sin }^{-1}\left[\frac{2}{\sqrt{5}}\right]$

Q. An $U-$ tube of base length ${}^{\prime }{l}^{\prime }$ filled with the same volume of two liquids of densities $\rho$ and $2\rho$ is moving with an acceleration ${}^{\prime }{a}^{\prime }$ on the horizontal plane, as shown in the figure. If the difference in heights of the liquid columns in the two vertical limbs (open to the atmosphere) is zero, then the height $h$ is given by

1. $\frac{al}{2g}$
2. $\frac{3al}{2g}$
3. $\frac{al}{g}$
4. $\frac{2al}{3g}$

Q. Identify the figure which represents the acceleration of a fluid along horizontal direction:

1. 
2. 
3. 
4. 

Q. The closed container filled with water is moving with some acceleration as shown in the figure. Then $P_A-P_D$ is :-

1. $-4\times {10}^3{\text{N/m}}^2$
2. $+4\times {10}^3{\text{N/m}}^2$
3. $+5.6\times {10}^5{\text{N/m}}^2$
4. $-5.6\times {10}^4{\text{N/m}}^2$

Q. The minimum horizontal acceleration (in ${\text{ms}}^{-2}$) of the container filled with water upto height of $2\text{m}$ as shown, so that the pressure at point $A$ of the container becomes atmospheric is (the tank is of sufficient height)

Q. Identify the figure which represents the acceleration of a fluid along horizontal direction:

Q. Width of the base of the accelerated container shown in the figure is: [Assume $g=10{\text{m/s}}^2$]

1. $10\text{m}$
2. $5\text{m}$
3. $6\text{m}$
4. $8\text{m}$

Q. When a half filled water tanker accelerates, the pressure on the back wheel increases.

1. True
2. False

Q. A given shaped glass tube having uniform cross-section is filled with water and is mounted on a rotatable shaft as shown in figure. If the tube is rotated with a constant angular velocity $\omega$, then

1. water levels in both section $A$ and $B$ go up
2. water level in section $A$ goes up and that in $B$ comes down
3. water level in section $A$ comes down and that in $B$ it goes up
4. water level remain same in both sections

Q. An $U-$ tube of base length ${}^{\prime }{l}^{\prime }$ filled with the same volume of two liquids of densities $\rho$ and $2\rho$ is moving with an acceleration ${}^{\prime }{a}^{\prime }$ on the horizontal plane, as shown in the figure. If the difference in heights of the liquid columns in the two vertical limbs (open to the atmosphere) is zero, then the height $h$ is given by

1. $\frac{al}{2g}$
2. $\frac{3al}{2g}$
3. $\frac{al}{g}$
4. $\frac{2al}{3g}$

Q. Angle of inclination of the water surface from horizontal for the given accelerated container shown in the figure is [Assume $g=10{\text{m/s}}^2$]

1. ${45}^{\circ }$
2. ${30}^{\circ }$
3. ${60}^{\circ }$
4. ${70}^{\circ }$

Q. A solid sphere of mass $m=2\text{kg}$ and specific gravity $s=0.5$ is held stationary relative to a tank filled with water. The tank is accelerating vertically upwards with $2{\text{m/s}}^2$. Choose the correct option(s):

1. Tension is the thread is $24\text{N}$
2. Tension in the thread is $28\text{N}$
3. If the thread snaps, acceleration of the sphere is $14{\text{m/s}}^2$
4. If the thread snaps, acceleration of the sphere is $16{\text{m/s}}^2$

Q.

A vessel containing water is given a constant acceleration ‘a’ towards the right along a straight horizontal path. Which of the following diagrams in the figure represents the surface of the liquid?

1. 

2. 

3. 

4. None of the above

Q. A closed cubical vessel is given a horizontal acceleration $a$. Find the value of $a$ such that pressure at the mid point $M$ of $\text{AC}$ is equal to pressure at $N$.

1. $2g$
2. $3g$
3. $g$
4. $4g$

Q. If area of cross-section of both the limbs are equal, find the difference in heights of the liquid in the two limbs when the system is given an acceleration of $2{\text{m/s}}^2$ in horizontal direction as shown in figure. Neglect the width of the limbs.

1. $15\text{cm}$
2. $18\text{cm}$
3. $20\text{cm}$
4. $10\text{cm}$

Q. Difference in heights between the liquid columns in the vertical limbs of an accelerated $U$-tube as shown in the figure is:
[Take $g=10{\text{m/s}}^2$]

1. $3\text{m}$
2. $5\text{m}$
3. $4\text{m}$
4. $2\text{m}$

Q. A given shaped glass tube having uniform cross-section is filled with water and is mounted on a rotatable shaft as shown in figure. If the tube is rotated with a constant angular velocity $\omega$, then

1. water levels in both section $A$ and $B$ go up
2. water level in section $A$ goes up and that in $B$ comes down
3. water level in section $A$ comes down and that in $B$ it goes up
4. water level remain same in both sections

Q. The tension in a string holding a solid block $({\rho }_b=700{\text{kg/m}}^3)$ below the surface of a liquid $({\rho }_l=1000{\text{kg/m}}^3)$ as shown in figure is $10\text{N}$ when the system is at rest. What will be the tension in the string if the system has an upward acceleration of $5{\text{m/s}}^2$?
$[\text{Take}g=10{\text{m/s}}^2]$

1. $10\text{N}$
2. $20\text{N}$
3. $15\text{N}$
4. $5\text{N}$

Q. A solid sphere of mass $m=2\text{kg}$ and specific gravity $s=0.5$ is held stationary relative to a tank filled with water. The tank is accelerating vertically upwards with $2{\text{m/s}}^2$. Choose the correct option(s):

1. Tension is the thread is $24\text{N}$
2. Tension in the thread is $28\text{N}$
3. If the thread snaps, acceleration of the sphere is $14{\text{m/s}}^2$
4. If the thread snaps, acceleration of the sphere is $16{\text{m/s}}^2$