Accelerating Containers

Q. When a large bubble rises from the bottom of a lake to the surface. Its radius doubles. If atmospheric pressure is equal to that of column of water height H, then the depth of lake is

1. H
2. 2H
3. 7H
4. 8H

Q. The coefficient of apparent expansion of a liquid when determined using two different vessels A and B are ${\gamma }_1$ and ${\gamma }_2$ respectively. If the coefficient of linear expansion of the vessel $A$ is $\alpha$, then the coefficient of linear expansion of vessel $B$ is found to be $\frac{{\gamma }_1-{\gamma }_2+3\alpha }{x}$. The value of $x$ is

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.

An air bubble of radius $1cm$ in water has an upward acceleration $9.8cm{s}^{-2}$. The density of water is $1gmc{m}^{-3}$ and water offers negligible drag force on the bubble. The mass of the bubble is ($g=980cm/s^2$).

1. $1.52gm$

2. $4.51gm$

3. $3.15gm$

4. $4.15gm$

Q.

A particle of mass m is projected with a speed u at an angle $\theta$ with the horizontal. Find the torque of the weight of the particle about the point of projection when the particle is at the highest point.

Q.

An object is located $2km$ beneath the surface of the water. If the fractional compression$∆V/V$is $1.36\%$ , the ratio of hydraulic stress to the corresponding hydraulic strain will be ……..

1. $2.26\times {10}^{9}N{m}^{-2}$

2. $1.96\times {10}^{7}N{m}^{-2}$

3. $1.44\times {10}^{7}N{m}^{-2}$

4. $1.44\times {10}^{9}N{m}^{-2}$

Q. Difference in height of the liquid columns in the limbs of a rotating $U-$ tube as shown in the figure is:
(Neglect the width of each limb and take $g=10{\text{m/s}}^2$)

1. $1\text{m}$
2. $0.8\text{m}$
3. $0.5\text{m}$
4. $0.6\text{m}$

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

Q.

Water flows out of a big tank along a horizontal tube AB of length l and radius r and bent at right angles at the other end as shown in the figure. The rate of flowis Q m³ /s. Calculate the moment of the force exerted by the water on the tube about the end A.

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 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. 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. Liquid surface in a rotating fluid about its axis is of the shape of

1. Ellipsoid
2. Sphere
3. Parabola
4. Paraboloid

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. An open square tank of side $1m$ is completely filled with water. If the tank is moved with an acceleration of $10m{s}^2$, find the slope of the free surface of water with the horizontal and the quantity of water which will spill out of the tank.

1. $1,0.5{\text{m}}^3$
2. $1,0.7{\text{m}}^3$
3. $3,0.7{\text{m}}^3$
4. $2,0.5{\text{m}}^3$

Q. A liquid is kept in a cylindrical vessel which is being rotated about a vertical axis through the centre of the circular base. If the radius of the vessel is r and angular velocity of rotation is $\omega$ , then the difference in the heights of the liquid at the centre of the vessel and the edge is

1. 
2. 
3. 
4. 

Q. An L-shaped glass tube is kept inside a bus that is moving with constant acceleration. During the motion, level of the liquid in the left arm is at $12\text{cm}$ whereas in the right arm, it is at $8\text{cm}$ when the orientation of the tube is as shown. Assuming that the diameter of the tube is much smaller than the levels of the liquid and neglecting effects of surface tension, the acceleration of the bus will be $\left({\text{g=10 m/s}}^2\right)$

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

Q.

Two light balls are suspended with light strings very close to each other. What happens when we blow air between the balls?

Q. A gardener waters plants by a pipe of diameter 1cm the water comes out at rate of 20cm×cm×cm÷s the reaction force on hand is 0.0051N

Q.

A liquid wets a solid completely. The meniscus of the liquid in a sufficiently long tube is

1. Convex

2. Cylindrical

3. Concave

4. Flat

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. Water flows in a horizontal tube as shown in figure. The pressure of water changes by $600N/m^2$ between x and y where the areas of cross section are $3c{m}^2$ and $1.5c{m}^2$ respectively. Find the rate of flow of water through the tube.

1. $169c{m}^3/s$
2. $179c{m}^3/s$
3. $189c{m}^3/s$
4. $199c{m}^3/s$

Q. If the container filled with liquid gets accelerated horizontally, find the value of acceleration $a$ for which point $x$ is exposed to air as shown in the figure.

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

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. Three liquids having densities ${\rho }_1$, ${\rho }_2$ and ${\rho }_3$ are filled in a $U\text{tube}$. The length of each liquid column is equal to $l$, ${\rho }_1>{\rho }_2>{\rho }_3$ and liquids remain at rest (relative to the tube) in the position shown in the figure. It is possible that

1. $U\text{tube}$ is accelerating leftwards
2. $U\text{tube}$ is accelerating upwards with acceleration $g$
3. $U\text{tube}$ is moving with a constant velocity
4. None of the above

Q.

A vertical off-shore structure is built to withstand a maximum stress of 10⁹ Pa. Is the structure suitable for putting up on top of an oil well in the ocean? Take the depth of the ocean to be roughly 3 km, and ignore ocean currents.

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. For the rotating container shown in figure, differences in the heights of the fluid between the centre and the sides (in $\text{cm}$) is-
[Take ${\pi }^2=10\&g=10{\text{m/s}}^2$ for calculation]

1. $12.5\text{cm}$
2. $18\text{cm}$
3. $15\text{cm}$
4. $20\text{cm}$

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

1. 
2. 
3. 
4. 

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