IISER Physics - Mechanical Properties of Fluids
Exam Duration: 45 Mins Total Questions : 25
An ice block with relative density 0.9 floats in water (density=1.0 g/cc). A part of block is outside water level. When the ice block has completely melted, the water level will
- (a)
rise
- (b)
fall
- (c)
remain same
- (d)
it will depend on mass of block
A piece of iron has weight win air, w1 when immersed completely in water and w2 when immersed completely in a liquid. The relative density of liquid is
- (a)
\(\frac { { w }_{ 1 }-{ w }_{ 2 } }{ w-{ w }_{ 1 } } \)
- (b)
\(\frac { { w }_{ 1 }-{ w }_{ 2 } }{ w-{ w }_{ 2 } } \)
- (c)
\(\frac { { w }-{ w }_{ 1 } }{ w-{ w }_{ 2 } } \)
- (d)
\(\frac { { w }-{ w }_{ 2 } }{ w-{ w }_{ 1 } } \)
In absence of gravity, which of the following will not be there for a fluid?
- (a)
Viscosity
- (b)
Surface tension
- (c)
Pressure
- (d)
Archimedes' upwards thrust
A body is just floating in a liquid. Both have same densities (i.e., body and liquid). If body is slightly pressed down and then released it will
- (a)
oscillate
- (b)
sink down
- (c)
come back to same position instantaneously
- (d)
come back to same position slowly
Along streamline,
- (a)
the velocity of a fluid particle remains constant
- (b)
velocity of all fluid particles crossing a given position is constant.
- (c)
the velocity of all fluid particles at a given instant is constant
- (d)
the speed of a fluid particle remains constant
An ideal fluid flows through a pipe of circular cross - section mad of two sections with diameters 2.5 cm and 3.75 cm. The ratio of velocities in the two pipes is
- (a)
\(9:4\)
- (b)
\(3:2\)
- (c)
\(\sqrt { 3 } :\sqrt { 2 } \)
- (d)
\(\sqrt { 2 } :\sqrt { 3 } \)
A cylinder of radius ris filled with water upto a height h, so that thrust on the walls is equal to that on bottom, then it is equal to
- (a)
\(\frac { R }{ 2 } \)
- (b)
\(R\)
- (c)
\(\frac { R }{ 3 } \)
- (d)
\(2R\)
A sphere of mass m falls through a viscous fluid with the terminal velocity v. Then, the terminal velocity of another sphere curved out of same material but mass 27 m is
- (a)
3v
- (b)
6v
- (c)
27v
- (d)
9v
When a number of small droplets combine to form a large drop, then
- (a)
energy is released
- (b)
energy is absorbed
- (c)
cannot be predicted
- (d)
process does not involve any energy change
A mercury drop of radius 10 cm is broken in 103 drops of equal size. The work done of equal size. The work done required in this process is (S=40X10-2 N/m)
- (a)
0.45 J
- (b)
0.9 J
- (c)
0.38 J
- (d)
0.72 J
A capillary is immersed in water in the absence of gravity. The water will
- (a)
rise to maximum height available
- (b)
rise to a height same as in presence of gravity
- (c)
not rise at all
- (d)
rise to a height lesser than that observe under gravity
A liquid drop of radius R breaks into N smaller droplets of radii r. If liquid has density \(\rho \) , specific tension T, then the drop in temperature is given by
- (a)
\(\frac { NT }{ \rho S } \left( \frac { 1 }{ R } -\frac { 1 }{ r } \right) \)
- (b)
\(\frac { NT }{ \rho S } \left( \frac { R }{ r } -1 \right) \)
- (c)
\(\frac { 3 }{ 4 } \frac { T }{ \rho S } \left( \frac { 1 }{ R } -\frac { 1 }{ r } \right) \)
- (d)
\(\frac { 3T }{ \rho S } \left( \frac { 1 }{ R } -\frac { 1 }{ r } \right) \)
A water drop of 0.01 cm3 is squeezed between the two glass plates and spread into an area of 20 cm2 . If surface tension of water is 7X10-2 N/m, the normal force required to separate the glass plates from each other will be
- (a)
56 N
- (b)
28 N
- (c)
36 N
- (d)
72 N
A closed tank has pressure, P=3 atm some point O on the tank. If tank is ruptured at this point to make a small hole, the velocity of efflux through the hole is ( 1 atm = 105 N/m2)
- (a)
10 m/s
- (b)
15 m/s
- (c)
20 m/s
- (d)
30 m/s
Wooden ball of density \(\rho \) is immersed in a liquid of density \({ \rho }^{ \prime }\) to a depth h below the surface of water and then released. The height to which the ball will come out of water is
- (a)
\(\left( \frac { \rho ' }{ \rho } -1 \right) h\)
- (b)
\(\left( \frac { \rho }{ \rho ' } -1 \right) h\)
- (c)
\(\left( 1-\frac { \rho ' }{ \rho } \right) h\)
- (d)
\(\left( 1+\frac { \rho ' }{ \rho } \right) h\)
An ice cube containing a stone inside it, is floating in water contained in a flask. The position of the level of water in the flask, when the whole ice melts, will be
- (a)
less than before
- (b)
greater than before
- (c)
remain same
- (d)
None of the above
A body has weight W1 in liquid of density \({ \rho }_{ 1 }\) and W2 in a liquid of density \({ \rho }_{ 2 }\) . The weight of the body in a liquid of density \({ \rho }_{ 3 }\) is
- (a)
\(\frac { { w }_{ 2 }({ \rho }_{ 3 }-{ \rho }_{ 1 })-{ w }_{ 1 }({ \rho }_{ 3 }-{ \rho }_{ 2 }) }{ { \rho }_{ 2 }-{ \rho }_{ 1 } } \)
- (b)
\(\frac { { w }_{ 1 }({ \rho }_{ 3 }-{ \rho }_{ 1 })-{ w }_{ 2 }({ \rho }_{ 3 }-{ \rho }_{ 2 }) }{ { \rho }_{ 2 }-{ \rho }_{ 1 } } \)
- (c)
\(\frac { { w }_{ 1 }({ \rho }_{ 3 }-{ \rho }_{ 1 })-{ w }_{ 2 }({ \rho }_{ 2 }-{ \rho }_{ 3 }) }{ { \rho }_{ 1 }-{ \rho }_{ 2 } } \)
- (d)
\(\frac { { w }_{ 1 }({ \rho }_{ 1 }-{ \rho }_{ 3 })-{ w }_{ 3 }({ \rho }_{ 2 }-{ \rho }_{ 3 }) }{ { \rho }_{ 2 }-{ \rho }_{ 1 } } \)
Match the statement given in column I with their formula / definition given in column II and select the correct option in the choices given below
Column I | Column II | ||
---|---|---|---|
A. | Fluid flowing in a horizontal pipe | 1. | \(\frac { 2{ r }^{ 2 } }{ q } \frac { \left( \rho -\sigma \right) }{ \eta } \) |
B. | Height of liquid in capillary tube | 2. | \(P+\frac { 1 }{ 2 } \rho { v }^{ 2 }\) |
C. | Terminal velocity | 3. | \(\frac { 2scos\theta }{ r\rho g } \) |
- (a)
A B C 2 3 1 - (b)
A B C 1 3 2 - (c)
A B C 3 2 1 - (d)
A B C 1 2 3
Assume that a drop of liquid evaporates by decrease in its surface energy, so that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible? The surface tension is T, density of liquid is \(\rho \) and L is its latent heat of vaporization
- (a)
\(\frac { \rho L }{ T } \)
- (b)
\(\sqrt { \frac { T }{ \rho L } } \)
- (c)
\(\frac { T }{ \rho L } \)
- (d)
\(\frac { 2T }{ \rho L } \)
Work done in increasing the size of a soap bubble from radius of (3 to 5) cm is nearly (surface tension of soap solution = 0.03 Nm-1)
- (a)
\(0.2\pi \quad mJ\)
- (b)
\(2\pi \quad mJ\)
- (c)
\(0.4\pi \quad mJ\)
- (d)
\(4\pi \quad mJ\)
Water is flowing continuously from a tap having an internal diameter of 8\(\times\) 10-3 m. The water velocity as it leaves the tap is 0.4 ms-1 . The diameter of the water stream at a distance 2X10-1 m below the tap is close to
- (a)
7.5X10-3 m
- (b)
9.6X10-3 m
- (c)
3.6X10-3 m
- (d)
5.0X10-3 m
Two mercury drops (each of radius r) merge to form a bigger drop. The surface energy of the bigger drop, if T is the surface tension, is
- (a)
\({ 2 }^{ 5/3 }\pi { r }^{ 2 }T\)
- (b)
\(4\pi { r }^{ 2 }T\)
- (c)
\(2\pi { r }^{ 2 }T\)
- (d)
\({ 2 }^{ 8/3 }\pi { r }^{ 2 }T\)
If a ball of steel (density \(\rho =7.8g\) cm-3) attains a terminal velocity of 10 cms-1 when falling in a tank of water (coefficient of viscosity \({ \eta }_{ water }=8.5\times { 10 }^{ -4 }\) Pa -s) then, its terminal velocity for glycerine \((\rho =12g{ cm }^{ -3 },\eta =13.2Pa-s)\) would be nearly
- (a)
1.6X10-5 cms-1
- (b)
6.625X10-4cms-1
- (c)
6.45X10-4cms-1
- (d)
1.5X10-5cms-1
A spherical solid ball of volume V is made of a material of density \({ \rho }_{ 1 }\) . It is falling through a liquid of density \({ \rho }_{ 2 }({ \rho }_{ 2 }<{ \rho }_{ 1 })\) . [Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed v, i.e., Fviscous= -Kv2(K>0)]. The terminal speed of the ball is
- (a)
\(\sqrt { \frac { Vg({ \rho }_{ 1 }-{ \rho }_{ 2 }) }{ k } } \)
- (b)
\(\frac { Vg{ \rho }_{ 1 } }{ k } \)
- (c)
\(\sqrt { \frac { Vg{ \rho }_{ 1 } }{ k } } \)
- (d)
\(\frac { Vg({ \rho }_{ 1 }-{ \rho }_{ 2 }) }{ k } \)
The terminal speed of a sphere of gold (density=19.5 kg m-3) is 0.2 ms-1 in a viscous liquid (density=1.5kg m-3). The terminal speed of a sphere of silver (density = 10.5 kg/m3) of the same size in the same liquid will be
- (a)
0.4 ms-1
- (b)
0.133 ms-1
- (c)
0.1 ms-1
- (d)
0.2 ms-1