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Class 11

Physics

Mechanical Properties of Fluids

Pressure and density

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Question

Medium

Solving time: 3 mins

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Book:

Mechanics Volume 2 (DC Pandey)

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Text solutionVerified

Writing pressure equation along the path

PMO

p_{P} + ρ g y - \frac{ρ ω ^{2} x ^{2}}{2} = p_{O}

Points

P

and

O

are open to atmosphere.
So, pressures at these points are same (= atmospheric pressure). Therefore, the above equation becomes,

ρ g y - \frac{ρ ω ^{2} x ^{2}}{2} = 0 or y = (\frac{ω ^{2}}{2 g}) x^{2}

This is the required parabolic equation of free surface of liquid.

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Practice questions from Mechanics Volume 2 (DC Pandey)

Question 1

Medium

A drop of liquid of radius

R = 1 0^{- 2} m

having surface tension

S = \frac{0.1}{4 π} Nm^{- 1}

divides itself into

K

identical drops. In this process the total change in the surface energy

Δ U = 1 0^{- 3}

J. If

K = 1 0^{α}

, then the value of

α

Topic:

Mechanical Properties of Fluids

Book:

Mechanics Volume 2 (DC Pandey)

View 2 solutions

Question 2

Medium

A glass plate of length

10 cm

, breadth

1.54 cm

and thickness

0.20 cm

weighs

8.2 gm

in air. It is held vertically with the long side horizontal and the lower half under water. Find the apparent weight of the plate. Surface tension of water

= 73

dyne per

cm, g = 980 cm / sec^{2}

Topic:

Mechanical Properties of Fluids

Book:

Mechanics Volume 2 (DC Pandey)

View solution

Question 3

Medium

The area of cross-section of a large tank is

0.5 m^{2}

. It has an opening near the bottom having area of cross-section

1 cm^{2}

. A load of

20 kg

is applied on the water at the top. Find the velocity of the water coming out of the opening at the time when the height of water level is

50 cm

above the bottom. (Take

g = 10 m / s^{2}

)

Topic:

Mechanical Properties of Fluids

Book:

Mechanics Volume 2 (DC Pandey)

View 3 solutions

Question 4

Easy

Assertion : At depth

h

below the water surface pressure is

p

. Then at depth

2 h

pressure will be

2 p

. (Ignore density variation).
Reason : With depth pressure increases linearly.
Directions : Choose the correct option.

If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
If Assertion is true, but the Reason is false.
If Assertion is false but the Reason is true.

Topic:

Mechanical Properties of Fluids

Book:

Mechanics Volume 2 (DC Pandey)

View solution

Practice more questions from Mechanical Properties of Fluids

Question 1

Hard

A conical vessel without a bottom stands on a table. A liquid is poured with the vessel \& as soon as the level reaches

h

, the pressure of the liquid raises the vessel. The radius of the base of the vessel is

R

and half angle of the cone is

α

and the weight of the vessel is

W

. What is the density of the liquid?

Topic:

Mechanical Properties of Fluids

Book:

Physics Galaxy Mechanics Vol 1 (Ashish Arora)

View 3 solutions

Question 2

Easy

Relative density of an oil is 0.8. Find the absolute density of oil in

CGS

and

S I

units.

Topic:

Mechanical Properties of Fluids

Book:

Mechanics Volume 2 (DC Pandey)

View 2 solutions

Question 3

Medium

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

ω

, then the difference in the heights of the liquid at the centre of the vessel and the edge is:

$\frac{r ω}{2 g}$
$\frac{r ^{2} ω ^{2}}{2 g}$
$2 g r ω$
$\frac{ω ^{2}}{2 g r ^{2}}$

Topic:

Mechanical Properties of Fluids

Book:

Fundamentals of Physics, Extended

View 2 solutions

Question 4

Easy

A vessel, whose bottom has round holes with diameter of

0.1 mm

, is filled with water. The maximum height to which the water can be filled without leakage is
(S.T. of water

= 75

dyne

/ cm, g = 1000 cm / s^{2}

)

$100 cm$
$75 cm$
$50 cm$
$30 cm$

Topic:

Mechanical Properties of Fluids

Book:

Fundamentals of Physics, Extended

View 7 solutions

Practice questions on similar concepts asked by Filo students

Question 1

"Please help with questions 3 and 4 as well as filling out the chart. Thank you! 3) Consider the following debate between two students. Students 1 think a star with an apparent magnitude number of-2.0 would look brighter than a star with an apparent magnitude number of+1.0. Student 2 disagree. You don't understand the number scale for apparent and absolute magnitude: The bigger the number the brighter the star Sg the +1.0 star would look brighter than the -2.0 star Do you agree or disagree with either or both of the students? Explain your reasoning: 4) Star Y appears much brighter than Star Z when viewed from earth but is found to be much less luminous: Assign a set of possible values for the apparent and absolute magnitudes of these stars that would be consistent with the information given in the previous statement Star Y Star Z m M"

Topic:

Physics

View solution

Question 2

Two coils in a network are positioned such that there is

100%

coupling between them. If the inductance of one coil is

10 mH

and the mutual inductance is

6 mH

, compute the inductance of the other coil.

Topic:

Physics

View solution

Question 3

Q 6.

A = 3 \hat{i} + 4 \hat{j} + 2 \hat{k}, B = 6 \hat{i} - \hat{j} + 3 \hat{k}

. Find a vector parallel to

A

whose magnitude is equal to that of

B

$\frac{46}{29} (3 \hat{i} + 4 \hat{j} + 2 \hat{k})$
$\frac{46}{29} (6 \hat{i} - \hat{j} + 3 \hat{k})$
$\frac{29}{46} (3 \hat{i} + 4 \hat{j} + 2 \hat{k})$
none

Topic:

Modern Physics

View solution

Question 4

Gurukripa XI-Foundation - DPI cAreer irstitute NLM \&F 1. एक गाड़ी

A

निसका द्रव्यमान

36 kg

है, पर चिश्रानुसार दो गुठके

B

तथा 4.

C

जिनके द्रव्यमान क्रमश:

10 kg

तथा

4 kg

है, जुडे हुए है। गाड़ी पर्रणहीन सतह पर गतिशील है। गाड़ी पर आरोपित बल

F

की गणना कीजिए जिसके लिए गुटके गाड़ी के सापेक्ष नहीं फिसले (गाड़ी के सापेक्ष विरामावस्था में रहें) (1)

150 N

(2)

200 N

(3)

240 N

(4)

40 N

2. लकड़ी के दो गुटके एक चिकनी क्षैतिज सतह पर इस प्रकार गतिशील है कि

m

द्रव्यमान का गुटका

M

द्रव्यमान के गुटके के सापेक्ष स्थिर रहता है, जैसा कि चित्र में दर्शाया गया है। बल

P

का परिमाण है- (1)

(M + m) g tan β

(2)

g tan β

(3)

m g cos β

(4)

(M + m) g cosec β

3. चित्र में,

60 N

भार का एक गुटका एक खुरदरी सतह पर रखा है। कि गुटके व सतह के मध्य घर्षण गुणांक

0.5

है। भार

W

का मान क्या होना चाहिये जिससे कि गुटका सतह पर न फिसले- (1)

μg

(3)

\frac{m}{μg}

5 kg

की तथा रस्सी (1)

60 N

(2)

\frac{60}{2} N

(3)

30 N

(4)

\frac{30}{2} N

(3) GCl GCl (P) Ltd., Jyoti Nagar, Piprali Road, Sika

Topic:

Mechanics

View solution

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Question Text
Topic	Mechanical Properties of Fluids
Subject	Physics
Class	Class 11
Answer Type	Text solution:1
Upvotes	106

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