Variation of Pressure in Fluids

Q.

Calculate the pressure exerted by water at the depth of 10 m.The density of water is $10kg/m^3$, and $g=10m/s^2$

Q.

Two vessels have the same base area but different shapes. The first vessel takes twice the volume of water that the second vessel requires to fill upto a particular common height. Is the force exerted by the water on the base of the vessel the same in the two cases? If so, why do the vessels filled with water to that same height give different readings on a weighing scale?

Q.

In problem 10.9, if 15.0 cm of water and spirit each are further poured into the respective arms of the tube, what is the difference in the levels of mercury in the two arms? (Specific gravity of mercury = 13.6)

Q.

A tank $5m$ high is filled with water up to $3m$ then is filled to the top with oil of density $0.85\raisebox{1ex}{$g$}\!\left/ \!\raisebox{-1ex}{$c{m}^3$}\right.$. Calculate the total pressure at the bottom of the tank due to these liquids.

Q.

The density $\rho$ of water of bulk modulus B at a depth y in the ocean is related to the density at surface by the relation

1. 

2. 

3. 

4. 

Q. A cylinder has a radius $10\text{cm}$. What height should it be filled with water so that the thrust at its walls is equal to that on its bottom?

1. $10\text{cm}$
2. $0.2\text{cm}$
3. $2.5\text{cm}$
4. $20\text{cm}$

Q. Consider a rectangular tank of size $(l\times b)$ filled with a liquid of density $\rho$, to a height $H$, as shown in the figure. Find the ratio of the force acting on the base to that on the walls of the tank.

1. $\frac{l}{H}$
2. $\frac{2l}{H}$
3. $\frac{l}{2H}$
4. $\frac{2l}{3H}$

Q.

A denser liquid exerts ________ pressure.

Q.

Explain why
a) The blood pressure in humans is greater at the feet than at the brain.

b) Atmospheric pressure at a height of about 6 km decreases to nearly half of its value at the sea level, though the height of the atmosphere is more than 100 km.

c) Hydrostatic pressure is a scalar quantity even though pressure is force divided by area.

Q. Ice of water at ${100}^o$ is given 540 cal of beat and the steam formed occupation 1671 cc at the atmosphere pressure. Then workdone against atmosphere pressure in this procces is nearly

1. 540 cal
2. 500 cal
3. 40 cal
4. 100 cal

Q. Mass of a body remains constant anywhere in the universe. State whether the statement is true or false.

1. True
2. False
3. Either
4. Neither

Q. In a car lift compressed air exerts a force F, on a small piston having a radius of 5 cm. This pressure is transmitted to a second piston of radius 15 cm. If the mass of the car to be lifted is 1500 kg, What is $F_1$? What is the pressure required to do this task?

Q. An iceberg is floating in water. The density of ice in the iceberg is $917kg{m}^{-3}$ and the density of water is $1024kg{m}^{-3}$. What percentage fraction of the iceberg would be visible?

1. $5\%$
2. $11\%$
3. $12\%$
4. $8\%$

Q. Derive the relation between surface tension and surface energy per unit area.

Q.

The maximum value of water pressure in the box in which water is filled upto a height of $4m$ is equal to (atmospheric pressure $={10}^{5}N/m^2,$ density of water $=1000kg/m^3$, $g=10m/s^2$)

1. 0.14 MPa
2. 1.4 MPa
3. 0.014 MPa
4. 0.104 MPa

Q. Assertion :A balloon filled with hydrogen stops rising after it has attained a certain height in the sky. Reason: As height increases, density of air decreases resulting in increase of buoyant force.

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Assertion is incorrect but Reason is correct

Q.

At what depth below the surface of water will the pressure be equal to 1 atmosphere. The atmospheric pressure is ${10}^{5}Pa$. Take density of water as ${10}^{3}kg{m}^{-3}$and $g=9.8m{s}^{-2}$.

Q. A bucket of water is hung from a spring balance. A piece of iron is suspended in the water without touching the sides or touching the bottom of the bucket. The reading of the spring balance

Q. Pressure is also measured in

1. mm of Hg
2. Joule
3. mm of Ag
4. Metre

Q.

State the factors which determine pressure at a point in a fluid.

Q. A block of wood of density $500kg/m^3$ has mass $mkg$ in air. A lead block which has apparent weight of $28kg$ in water is attached to the block of wood, and both of them are submerged in water. If their combined apparent weight in water is $20kg$, find the value of $m$. Taken density of water $=1000kg/m^3$.

Q. A steel rod has a radius $10mm$ and a length $2m$. A force strtches it along its length and produes a strain of $0.30\%$. Youngs modulus of the steel is $2\times {10}^{11}N/m^2$. The magnitude of the force strething the rod is about

1. $94kN$
2. $188kN$
3. $201kN$
4. $402kN$

Q. Why is the bottom part of the foundation of a building made wider?

Q. The pressure gauge shown in figure has a spring for which $k=60N/m$ and the area of the piston is $0.50c{m}^2$ . Its right end is connected to a closed container of gas at a gauge pressure of $30kPa$. How far will the spring be compressed in the region containing the spring is (a) in vacuum and (b) open to the atmosphere? Atmospheric pressure is $1001kPa$,

Q. A drop of some liquid of volume $0.04c{m}^3$ is placed on the surface of a glass slide. Then another glass slide is placed on it in such a way that the liquid forms a thin layer of area $20c{m}^2$ between the surfaces of the two slides. To separate the slides a force of $16\times {10}^5$ dyne has to be applied normal to the surfaces. The surface tension of the liquid is (in dyne-$c{m}^{-1}$):

1. $60$
2. $80$
3. $70$
4. $90$

Q. A $10meter$ long thick rubber pipe is suspended from one of its ends. The extension produced in the pipe under its own weight will be :$(Y=5\times {10}^{6}N/m^2$ and density of rubber =$1500kg/m^3$)

1. $0.15m$
2. $0.0015m$
3. $0.015m$
4. $1.5m$

Q. Two masses 7 kg and 12 kg are connected at the two ends of a light inextensible string over a frictionless pulley. Find the acceleration of the masses and the tension in the string, when the masses are released.

Q. A simple pendulum is first allowed to swing freely on Earth and then taken to the moon. Which of the following statements about the pendulum is correct?

1. The period of the pendulum on the moon is greater than it was on Earth
2. The frequency of the pendulum on the moon is greater than it was on Earth
3. The potential energy of the pendulum on the moon is greater than it was on Earth
4. The kinetic energy of the pendulum on the moon is greater than it was on Earth
5. The period, the frequency, the kinetic energy, and the potential energy of the pendulum on the moon are the same as they were on Earth

Q. A ceiling fan has a diameter (of the circle through the outer edges of the three blades) of 120 cm and rpm 1500 at full speed. Consider a particle of mass 1 g sticking at the outer end of a blade.
a. How much force does it experience when the fan runs at full speed?
b. Who exerts this force on the particle?
c. How much force does the particle exert on the blade along its surface?