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Mechanical Properties of Fluids

Pressure and density

A uniform rod of length b capable of tuning about its end whic

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Medium

Solving time: 3 mins

A uniform rod of length $b$ capable of tuning about its end which is out of water, rests inclined to the vertical. If its specific gravity is $5/9$ , find the length immersed in water.

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Book:

Physics Galaxy Mechanics Vol 1 (Ashish Arora)

Text solutionVerified

ρ . A . x (2 b - \frac{x}{2}) = 0.75 ρ A .2 b . b

2 b x = \frac{x ^{2}}{2} = \frac{3}{2} b^{2}

x = [b /3]

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A uniform rod of length

b

capable of tuning about its end which is out of water, rests inclined to the vertical. If its specific gravity is

5/9

, find the length immersed in water.

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Practice questions from Physics Galaxy Mechanics Vol 1 (Ashish Arora)

Question 1

Hard

A tank is filled with a liquid upto a height

H

. A small hole is made at the bottom of this tank. Let

t_{1}

be the time taken to empty first half of the tank and

t_{2}

the time taken to empty rest half of the tank. Then find

\frac{t _{1}}{t _{2}}

Topic:

Mechanical Properties of Fluids

Book:

Physics Galaxy Mechanics Vol 1 (Ashish Arora)

View 2 solutions

Question 2

Medium

A piece of ice is floating in a liquid. What happens to the level of liquid when all ice melts ?

level remains same if liquid is water
level falls if liquid is water
level will rise if liquid is denser than water
level will rise if liquid is lighter than water

Topic:

Mechanical Properties of Fluids

Book:

Physics Galaxy Mechanics Vol 1 (Ashish Arora)

View solution

Question 3

Medium

. The density of air in atmosphere decreases with height and can be expressed by the relation :

ρ = ρ_{0} e^{- A h}

where

ρ_{0}

is the density at sea-level,

A

is a constant and

h

is the height. Calculate the atmospheric pressure at sea-level. Assume

g

to be constant.

(g = 9.8 m / s^{2}, ρ_{0} = 1.3 kg / m^{3}

and

A = 1.2 \times 1 0^{- 4} m^{- 1})

Topic:

Mechanical Properties of Fluids

Book:

Physics Galaxy Mechanics Vol 1 (Ashish Arora)

View solution

Question 4

Medium

For the system shown in the figure the cylinder on the left at

L

has a mass of

600 kg

and a cross sectional area of

800 cm^{2}

. The piston on the right, at

S

, has cross sectional area

25 cm^{2}

and negligible weight. If the apparatus is filled with oil

(ρ = 0.75 gm / cm^{3})

Find the force

F

required to hold the system in equilibrium. Take

g = 10 m / s^{2}

Topic:

Mechanical Properties of Fluids

Book:

Physics Galaxy Mechanics Vol 1 (Ashish Arora)

View 3 solutions

Practice more questions from Mechanical Properties of Fluids

Question 1

Medium

A block of wood is held deep inside water. Its acceleration immediately after release is

2 ms^{- 2}

upwards. Find the relative density of the wood

[g = 10 ms^{- 2}]

Topic:

Mechanical Properties of Fluids

Book:

Physics for JEE Main and Advanced Mechanics 2 (McGraw Hill)

View solution

Question 2

Easy

Two blocks are floating in water. When they are brought sufficiently close they are attracted to each other due to surface tension effects. When the experiment is repeated after replacing water with mercury, once again the two blocks are attracted. Explain the phenomena. It is given that water wets the material of the block where as mercury does not.

Topic:

Mechanical Properties of Fluids

Book:

Problems in Physics I for IIT JEE (McGraw Hill)

View solution

Question 3

Easy

A large open tank has two holes in the wall. One is a square hole of side

L

at a depth

y

from the top and the other is a circular hole of radius

R

at a depth

4 y

from the top. When the tank is completely filled with water, the quantities of water flowing out per second from both holes are the same. Find the value of

R

Topic:

Mechanical Properties of Fluids

Book:

Physics Galaxy Mechanics Vol 1 (Ashish Arora)

View 8 solutions

Question 4

Easy

Two identical cylindrical vessels (area of cross-section

3.5 \times 1 0^{- 3} m^{2}

) with their bases at the same level contain liquid of density

800 kg / m^{3}

. The height of liquid in one vessel is

0.3 m

and in the other it is

0.1 m

. Assuming

g = 10 m / s^{2}

, find the workdone by gravity in equalising levels when the vessels are interconnected at bottom.

Topic:

Mechanical Properties of Fluids

Book:

Physics Galaxy Mechanics Vol 1 (Ashish Arora)

View solution

Practice questions on similar concepts asked by Filo students

Question 1

By equating the gravitational and centripetal acceleration at the equator of a rotating 1.4Mâ˜‰ neutron star, compute the minimum rotation period for such a star. Assume the star remains spherical with a radius of 10 km.

Topic:

Physics

View solution

Question 2

1. Wind turbines capture potential energy from the wind and convert it to electrical energy. True False 2. The Betz limit refers to the maximum height of the rotor on a wind turbine. True False 3. If the wind speed doubles, the wind power increases by a factor of four. True False 4. The power available from a wind turbine is proportional to the square of the rotor diameter. True False 5. Rotors of wind turbines are twisted along their length to provide a constant angle of attack to the wind. True False 6. A Savonius turbine utilizes drag force to capture wind energy. True False 7. A Darrieus wind turbine uses drag force to capture wind energy. True False 8. The acronym HAWT stands for horizontal axis wind turbine. True False 9. The blades of wind turbines can be designed to harness wind energy by creating a lift force or a drag force. True False 10. Typical components in a wind turbine nacelle include a gearbox, brake, generator, and flux capacitor. True False

Topic:

Physics

View solution

Question 3

Problem 2: Write the expression for the wavefunction of a harmonic wave of the amplitude 10 V/m, period 2.2 * 10^15 s, and speed 3 * 10^8 m/s. The wave is propagating in the negative x-direction and has a value of 10 V/m at t=0 and x=0.

Topic:

Physics

View solution

Question 4

Gill change in momentum of photons per unit time. i.e., force acting on photons, Ap, Ar =1 F.Acose. he 2h cose (7) 2h cose (i)=24cos³0(1) (ie in upward direction), Hence radiation pressure, P = 21A CA Case V: The radiation falling on the surface at certain angle and absorbed by the surface: In this case the momentum of photons will change in horizontal direction (x-direction) and venical direction (y-direction). psin 8 pcos e 6 #t Incident radiation Momentum of a photon, p= Considering in horizontal direction. Absorbed radiation -cos² 8 = 21 cos² e Normal Tangent ---- Initial momentum of one photon. (Panitial), = e in rightward direction) Final momentum of the photon, (Pinal), = 0 Change in momentum of one photon in horizontal direction, (45), -(Pro), -(Pita), -(sine) (i) (AP), -(P), (P), (AP), = 0-((*cose) (-1))-cose (1) (i.e. in upward direction) Energy incident per unit time (or power), E = LA cos8 Number of photons incident per unit time, IAcos@ IAcos@.) hf he A= Therefore, the total change in momentum of photons per u time, i.e. force acting on photons, =n=cose() F₁ = Ap, Ar IAcos@h he (i.e. in upward direction) Hence the vertical component of the radiation force on surface will be 21 cos¹8 in downward direction Sol in vertical direction, F, = Hence radiation pressure, P= LA *cos(7)=cos²8 (7) 214 cl cos 8==cos 8 21 ILLUSTRATION 5.6 (a) How many photons of a radiation of wavelength A 5 x 10¹ m must fall per second on a blackened plate order to produce a force of 6.62 x 10¹ N? (b) At what rate will the temperature of plate rise if its mass 19.86 kg and specific heat is equal to 2500 J kg K?

Topic:

Modern Physics

View solution

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Question Text	A uniform rod of length $b$ capable of tuning about its end which is out of water, rests inclined to the vertical. If its specific gravity is $5/9$ , find the length immersed in water.
Topic	Mechanical Properties of Fluids
Subject	Physics
Class	Class 11
Answer Type	Text solution:1
Upvotes	151