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Two blocks connected by a massless string slides down an inclined plane having an angle of inclination of 37°. The masses of the two blocks are M₁ = 4 kg and M₂ = 2 kg respectively and the coefficients of friction of M₁ and M₂ with the inclined plane are 0.75 and 0.25 respectively. Assuming the string to be taut, find the common acceleration of two masses

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Important Questions on Mechanical Properties of Fluids

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Surface Tension

Which one of the following statement is correct?

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Surface Tension

A rectangular film of liquid is extended from

(4 cm \times 2 cm)

(5 cm \times 4 cm)

. If the work done is

3 \times 10^{- 4} J

, the value of the surface tension of the liquid is

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Surface Tension

A soap bubble having radius of

1 m m

is blown from a detergent solution having a surface tension of

2.5 \times 10^{- 2} N m^{- 1} .

The pressure inside the bubble equals at a point

Z_{0}

below the free surface of water in a container. Taking

g = 10 m s^{- 2},

density of water

= 10^{3} k g m^{- 3},

the value of

Z_{0}

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Surface Tension

If a drop of liquid breaks into smaller droplets, it results in lowering of temperature of the droplets. Let a drop of radius

R

, break into

N

small droplets each of radius

r

, then decrease (drop) in temperature

Q

(given, specific heat of liquid drop

= S

and surface tension

= T

)

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Surface Tension

Two blocks ( $m = 0.5 kg$ and $M = 4.5 kg$ ) are arranged on a horizontal frictionless table as shown in the figure. The coefficient of static friction between the two blocks is $\frac{3}{7} .$ Then the maximum horizontal force that can be applied on the larger block so that the blocks move together is $N .$ (Round off to the Nearest Integer) [Take $g$ as $9.8 m s^{- 2}$ ]

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HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Surface Tension

When water is filled carefully in a glass, one can fill it to a height $h$ above the rim of the glass due to the surface tension of water. To calculate $h$ just before water starts flowing, model the shape of the water above the rim as a disc of thickness $h$ having semicircular edges, as shown schematically in the figure. When the pressure of water at the bottom of this disc exceeds what can be withstood due to the surface tension, the water surface breaks near the rim and water starts flowing from there. If the density of water, its surface tension and the acceleration due to gravity are $10^{3} kg m^{- 3}, 0.07 N m^{- 1}$ and $10 m s^{- 2}$ respectively, the value of $h$ (in $mm$ ) is ________.

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MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Surface Tension

The following observations were taken for determining surface tension

T

of water by capillary method:

diameter of capillary,

D = 1.25 \times 10^{- 2} m

rise of water,

h = 1.45 \times 10^{- 2} m

Using

g = 9.80 m s^{- 2}

and the simplified relation

T = \frac{r h g}{2} \times 10^{3} N m^{- 1}

the possible error in surface tension is closest to:

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Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Surface Tension

Derive Laplace’s law for a spherical membrane.

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Surface Tension

A box of mass

10 kg

is placed near the rear end of a long flat trolley such that it is

2 m

from its rear end. The coefficient of friction between the box and the trolley surface is

0.2

. Starting from rest, the trolley is given a uniform acceleration of

3 m s^{- 2}

. How much distance will the trolley cover by the time the box fell off from the trolley?

(g = 10 m s^{- 2})

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Surface Tension

A system of two blocks of masses $m = 2 kg$ and $M = 8 kg$ is placed on a smooth table as shown in figure. The coefficient of static friction between two blocks is $0.5$ . The maximum horizontal force $F$ that can be applied to the block of mass $M$ so that the blocks move together will be $(g = 9.8 m s^{- 2})$

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EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Surface Tension

A wire of length

10 cm

is gently placed horizontally on the surface of water having a surface tension of

75 \times 10^{- 3} N m^{- 1}

. What force is required to just pull up the wire from the water surface?

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Surface Tension

A block of mass $5 kg$ resting on a horizontal surface is connected by a cord, passing over a light frictionless pulley to a hanging block of mass $5 kg$ . The coefficient of kinetic friction between the block and the surface is $0.5$ . Tension in the cord is $(g = 9.8 m s^{- 2})$

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MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Surface Tension

Work done in increasing the size of a soap bubble from a radius of

3 cm

5 cm

is nearly (surface tension of soap solution

= 0.05 {Nm}^{- 1}

)

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Surface Tension

A small spherical droplet of density

d

is floating exactly half immersed in a liquid of density

ρ

and surface tension

T .

The radius of the droplet is (take note that the surface tension applies an upward force on the droplet):

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Surface Tension

Calculate the work done in increasing the radius of a soap bubble in air from 1 cm to 2 cm. The surface tension of the soap solution is 30 dyne/cm. $(π = 3.142)$

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Surface Tension

Given in the figure are two blocks

A

and

B

of weight

20 N

and

100 N

, respectively. These are being pressed against a wall by a force

F

and kept in equilibrium as shown. If the coefficient of friction between the blocks is

0.1

and between block

B

and the wall is

0.15

, the frictional force applied by the wall on block

B

is:

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Surface Tension

A thin metal wire of density

ρ

floats on water surface horizontally. If it is NOT to sink in water then maximum radius of wire is proportional to (

T =

surface tension of water,

g =

gravitational acceleration)

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Surface Tension

The radius

R

of the soap bubble is doubled under isothermal condition. If

T

be the surface tension of the soap bubble, the work done in doing so is given by

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Surface Tension

A block of mass

m_{2}

is placed on a horizontal table and another block of mass

m_{1}

is placed on top of it. An increasing horizontal force

F = α t

is exerted on the upper block but the lower block never moves as a result. If the coefficient of friction between the blocks is

μ_{1}

and that between the lower block and the table is

μ_{2}

, then what is the maximum possible value of

μ_{1} / μ_{2} ?

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Surface Tension

A system consists of three masses

m_{1}, m_{2}

and

m_{3}

connected by a string passing over a pulley

P .

The mass

m_{3}

hangs freely and

m_{2}

and

m_{1}

are on a rough horizontal table (the coefficient of friction

= μ) .

The pulley is frictionless and of negligible mass. The downward acceleration of mass

m_{3}

is: (Assume

m_{1} = m_{2} = m_{3} = m)

Important Questions on Mechanical Properties of Fluids

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